'one' doesn't have to be there.

Brackets (...) represent an omitted word.
2. and 3. are correct, as is 4.
5. Do you have any one car I
could use? (OK)
6. Do you have any one car I
can use? (OK if you have a disability.)
On the phone with a rent-a-car place
Max: Do you have any cars?
Agent: No. We don't
Max: Any one car? That is, it doesn't matter what kind or type of car it is.
Agent: Well, we have a few cars, but they're last year's model.
Max: That's OK, but I'm disabled, so do you have any one car that I can use? (i.e., have the ability to drive)