One of the engineers who design those programs is visiting with us today?
or
One of the engineers who designs those programs is visiting with us today?
One of the engineers who design those programs is visiting with us today?
or
One of the engineers who designs those programs is visiting with us today?
I would say:
One of the engineers designing those programs is visiting us today.
If you must include who, it should be:
One of the engineers who designs those programs is visiting us today.
The subject is singular, therefore, the verb should agree with one.
NOTE: I deleted the with because the engineers are not going somewhere with you, they are visiting you. If they are going someplace with you, you should say where you guys are visiting:
... visiting [insert person/place to be visited] with us.
Depends on the meaning!
(a)"One of the engineers who design those programs is visiting us today."
The relative clause specifies which group of 'the engineers' is referred to, here: the ones that "design those programs".
(b) "One of the engineers, who designs those programs, is visiting us today."
The relative clause gives additional information about 'one of the engineers'. You could then say: One of the engineers, who BY THE WAY designs those programs (...). The commas are obligatory!