Being omnipotent seems to only require having maximal power, which would only require the ability to make what is logically possible. — Naomi

Why would we an omnipotent supreme being have to abide by what we understand as logical or illogical? As freewhirl and Isaac242 were sayng, it seems like we are trying to force our human conceptions of reason and logic onto a supreme omnipotent being which would likely transcend our conceptions of these things. Omnipotence may not be logically possible but it also may not have to be since an omnipotent being could exist outside of time, space, and reason.

And I would also argue that, if god exists, he has done something that is, to us, logically impossible before. The creation of the universe ex nihilo seems to be an example of god doing something logically impossible. This states that god created the universe from nothing, no raw materials or pre-existent material whatsoever.

It is then implied by creatio ex nihilo that God can do/make something that is logically impossible because he has before. So for all we know, he can draw a square circle, we just may not be able to understand it.

This still leaves us with the paradox, but, to play devil's advocate here, the theist may have a third way out. The theist could appeal to his ability to do things which are logically impossible and argue that ipso facto we can not understand the extent of his power opting for an argument that looks something like this:
1. If god can do logically impossible things, then we will not be able to comprehend the extent of his omnipotent power
2. God can do logically impossible things
3. We will not be able to comprehend the extent of his omnipotent power (MP 1,2)