These usages aren't necessarily at odds, though I'd say that your explication of "irony" is unduly specific; it isn't precisely the opposite of what's expected so much as some sort of violation of expectation. In fact, I'd say that irony is at its best when the observed events aren't opposite expectation but skew to expectation.
When you think of it that way, an odd coincidence is conceivably justifiable as a weak case of irony, in that one ordinarily expects a lack of odd coincidences -- the normal expectation is that events with unrelated causes will have unrelated effects. (Not to say that this normal expectation is entirely valid.)