To supplement to the phrases cited by other answerers, I offer the following phrases not previously mentioned, organized chronologically from earliest first occurrence to latest first occurrence:
honest bone
From Tim Bobbin, "Village Events," in Tim Bobbin's Lancashire Dialect and Poems (September 1828):
Mary. Say! why by my troth it was fair cheating ; but it's just like their rascally tricks ; for there's not an honest bone in the hide of never a greasy tyke of 'em all.
idle bone
From Thomas Cooper, "Tim Swallow-whistle, The Tailor; or 'Every Dog Has His Day'," in Wise Saws and Modern Instances, volume 1 (1845):
He was full forty years old when the incidents occurred we are about to relate ; and up to that time, as he used himself to say, "Nobody could ever say he had an idle bone in his skin."
dishonest bone
From "Board of Supervisors," in the [San Francisco, California] Daily Alta California (May 3, 1870):
Mr. Badlam replied at some length, and spoke warmly against the measure. Shrader, he said, was always to vote away money; still, he would not say there was a dishonest bone in his body.
cruel bone
From William Thomes, The Belle of Australia, or Who Am I? serialized in Ballou's Dollar Monthly Magazine (November 1883):
Sure, he hasn't a cruel bone in his whole body, and he loves yer to distraction, and ivery night he drames of yer, or some one else, and calls yer name, and mourns for yer."
cowardly bone
From "Butler and Porter," in the Pittsburgh [Pennsylvania] Dispatch (May 19, 1889):
In your issue of May 5 I was very much surprised to find General Ben Butler accusing Admiral David D. Porter of cowardice and turning tail to the enemy. Now, I have had the honor of a command in the nary under Porter, and know that he has not a cowardly bone in his body.
deceitful bone
From Theodora Wilson & James Harvey, "After Many Days: An American Novel" (1892):
Rob's a little racketty, perhaps, but I never knew a man that had more friends. There's not a deceitful bone in his body.
bad bone
From Seumas MacManus, A Lad of the O'Friels (1903):
"Though I say it that maybe isn't expected to say it," said Corney Higarty generously, "he was a warrior and a brave fella, and hadn't a bad bone in his body. ...
scheming bone
From "Official Proceedings" in The American Pressman (September 1907):
Any one who knows John Hamilton, the introducer of the resolution in the St. Louis convention, knows he is the soul of honor, and if there is a scheming bone in his body I do not know it.
From C.N. Williamson & A.M. Williamson, The Powers and Maxine (1907):
You know Raoul hasn't a practical bone in his body. He will think I've deceived him, and nothing else will matter.
vicious bone
From Temple Bailey, "The Voice of Gold," in the Greencastle [Indiana] Herald (January 27, 1908):
"Timid!" Gloria stared. "Why, he hasn’t a timid bone in bis body, Aunt Caro."
From Emma Hewitt, How to Train Children (1908):
The boy hasn't a vicious bone in his body. I've known him ever since he was born. If he has suddenly developed this tendency, it is purely physical.
honorable bone
From "No Vacations, No Pleasure, Just Buttonholes!" in the Chicago [Illinois] Examiner (April 9, 1911):
I’ll tell you the truth about yourself. You’re a, creature not fit to be called a man. You haven’t got an honorable bone in your body.
pessimistic bone
From "Spirit of Optimism," in The Spectator (April 16, 1916):
There was not a pessimistic bone in his body. Bill was made of optimism.
good bone
From Henry Stephenson, Christie Bell of Goldenrod Valley: A Tale of Southern Indiana and of Cincinnati in the Old Time (1918):
"I tell you, Terence Macmannihan, Carmichael Bell is a failure—an utter failure. There isn't a good bone in his body. He hasn't a single point. ...
reckless bone
From "Martha Lee Says: Folks Never Seem to Pick Out the Right Mate" in the Indianapolis [Indiana] Times (June 15, 1926):
Here's a girl who has gone into marriage with all the requisites of a good housekeeper—and not a reckless bone in her.
generous bone
From Anne Green, The Selbys (1930) [snippet view]:
... tasks that go with it; you Americans are a nasty commercial race, not a generous bone in your bodies."
philanthropic bone
From Grace Oursier, Ex-mistress (1930) [combined snippets]:
At the age of forty-five, there wasn't a gray hair in his red head, nor a philanthropic bone in his body.
malicious bone
From an unidentified story in The Saturday Evening Post (1932):
"Of course he'll talk to Sue about you, and about being your wife's uncle. Well, Sue will be amused, but she'll not repeat it. There's not a malicious bone in her body."
friendly bone
From "Sorrow Comes to Hungry Gully: The Burrcutter and His Mate," in the [Sydney, New South Wales] Land (June 17, 1937):
"I hate, Fantod," declared Maudie. "There's not a friendly bone in his whole body. And Blue Horrors'11 be just as bad when he gets older. Like father, like son. Anyhow, they're insured."
kind bone
From Faith Baldwin, Temporary Address: Reno (1941) [cited quotation not shown in snippet window]:
You haven't a kind bone in your body or a selfless emotion. But I like you just the same.
dangerous bone
From Henry Lieferant & Sylvia Lieferant, Teacher's Husband (1941) [snippet view]:
"Then that's fine. Fred Dexter the housewife's friend. Always helpful—never a dangerous bone in his body. Good old Fred—"
lying bone
From an unidentified story in Detective Book Club Selections (1943) [combined snippets]:
"You heard what Roncie said. That ends the matter, do you understand? There isn't a lying bone in the girl's body, Bob. ...
truthful bone
From Dawn Powell, My Home Is Far Away (1944) [text not visible in snippet window]:
Her stepmother declared she never heard so much nonsense in all her life, and there wasn't a truthful bone in Marcia's whole body.
religious bone
From Louis Paul, Breakdown (1946) [snippet view]:
"He's a liar, my dear. He hasn't got a religious bone in his body."
vengeful bone
Jack Woodford & John Thompson, Honey (1951) [quoted text not visible in snippet window]:
There isn't a mean or vengeful bone in Honey's body and you'd only embarrass her. She has already forgiven you.
gracious bone
From Lily MacLeod, Return to Life (1951) [snippet view]:
There was not a gracious bone in my body. I knew it too, but I was powerless to do anything about it.
creative bone
From Edith Heal, The Shadow Boxers (1956) [snippet view]:
There wasn't a single creative bone in his body. His mind (he could see it sometimes when he sat with the bottle) was putty, abjectly willing to take on any shape that was suggested.
unkind bone
From Viña Delmar, "The Second Mrs. Thorpe," in The Saturday Evening Post (February 5, 1957) [combined snippets]:
He says, 'Underneath, Cammie means well. He actually hasn't an unkind bone in his body.' You understand, Mr. Cameron, I am quoting my husband. Personally I think you're just a natural-born jerk.
hostile bone
From an unidentified article in The Griffin (1960) [combined snippets]:
The gentle little "Irish" porter, Galy Gay, without an aggressive or hostile bone in his body, is transmogrified through a series of farcical events into one hell of a soldier.
spiritual bone
From Warren Miller, The Sleep of Reason: A Novel (1960) [combined snippets]:
He fixed himself a second drink, set the back of the unmodernized Morris chair at a forty-five-degree angle, and settled down with the Reverend Peter Paul's vigorous and forthright book. He groaned as he opened it. He had not a spiritual bone in his body.
courageous bone
From John Ehle, The Land Breakers (1964) [combined snippets]:
Her father had told him off, though. She hadn't thought he had a courageous bone in his body, and she guessed he didn't have but that one, the one he saved for old man Harrison.
pious bone
From John Gould, The Jonesport Raffle, and Numerous Other Maine Veracities (1969) [snippet view]:
He was a heathen, a pagan, an atheist, and anything else you want to call him, and he didn't have a pious bone in his body.
cynical bone
From Dick West, "The Lighter Side," in the [Palm Springs, California] Desert Sun (January 15, 1975):
But, thank God, I don’t have a cynical bone in my beautiful body. I always assume the officials in charge of these matters know what they are doing.
Combining the phrase inoted in this answer with the phrases cited in previous answers cited yields the following list, by year:
1826 "a lazy bone"
1828 "an honest bone"
1836 "a selfish bone"
1845 "an idle bone"
1858 "a mean bone"
1870 "a dishonest bone"
1882 "a jealous bone"
1883 "a cruel bone"
1889 "a cowardly bone"
1892 "a deceitful bone"
1903 "a bad bone"
1907 "a scheming bone"
1907 "a practical bone"
1908 "a timid bone"
1908 "a vicious bone"
1911 "an honorable bone"
1916 "a pessimistic bone"
1918 "a good bone"
1923 "an artistic bone"
1926 "a reckless bone"
1930 "a generous bone"
1930 "a philanthropic bone"
1932 "a malicious bone"
1937 "a friendly bone"
1941 "a kind bone"
1941 "a dangerous bone"
1943 "a lying bone"
1944 "a truthful bone"
1946 "a religious bone"
1951 "a vengeful bone"
1951 "a gracious bone"
1956 "a creative bone"
1957 "an unkind bone"
1960 "a hostile bone"
1960 "a spiritual bone"
1964 "a courageous bone"
1967 "a racist bone"
1969 "a pious bone"
1975 "a cynical bone"
Conclusions
It seems quite clear that "not a [modifier] bone in [one's] body" is a recurring and arguably idiomatic phrase in modern English. The particular wording "not a racist bone in [one's] body" seems to have arisen fairly late to the parade of related forms, but that is hardly surprising given that racism itself is a fairly young word—Merriam-Webster's Eleventh Collegiate Dictionary (2003) assigns it a first known occurrence date of 1933.
One further point of interest here is how heavily freighted toward positive meanings the phrase tended to be in the early decades of its use. From the period from 1826 to 1908, I found thirteen forms of "not a [modifier] bone" that were positive (starting with "not a lazy bone" in 1826) and just two that were negative (starting with "not an honest bone" in 1828), Over the period from 1911 to 1975, in contrast, I counted ten forms that were positive and fourteen that were negative. Even so, the overall count of individual forms tends in the direction of positive expressions—twenty-three to sixteen. I haven't attempted to count the total numbers of positive and negative instances, but during the nineteenth century, at least, most instances seem to have expressed approval of the person to whom the phrase was applied.
Although I searched for as many "[modifier] bone" phrases as I could think of, the list of above is obviously not exhaustive. Many other positive and negative formulations undoubtedly occur in speech or in print from time to time. Also, I selected 1975 as the last year to include in my database searches, as I was more interested in forms of the phrase that preceded "not a racist bone" chronologically than in forms that followed it.
Not+Minimal Direct ObjectNPI construction, like drink a drop, eat a bite, say a word, do a thing, lift a finger In this version, we're evaluating bones (or hairs) as minimal pieces of the body. Consequently any discussion of them that omits the negative is going to miss a lot. – John Lawler Jun 05 '23 at 13:09