The monotheistic Judeo-christian-islamic concept of God is that He is all powerful - omnipotent. This is often thought to mean that God can do anything. But most agree that this is not the case and will explain that God cannot do things which are logical contradictions and even fundamentalist Christians put out brochures entitled "5 things that God cannot do". So I think we can easily think up examples of things that God cannot do like set before us two apples which are also three apples. I think we could agree that God cannot make a plane figure that is both a circle and a square at the same time. God cannot do these things because the definitions of the words in these contradict each other. But these are not a coherent limitation upon God because these things are not even coherent things to do -- they acutally make no sense.
We do however have reason to be cautious because our understanding of logic may not be all that perfect or complete. The realities of quantum physics brought us face to face with this in a rather startling way in modern times. Thus the reality is that although we may be confident that God is constrained by the limits of logical consistency, we may not necessarily be entirely confident about what these limitations are exactly. I think the consequence of this that theists will immediately think of and agree with is that things that seem logically contradictory to us (like being both three persons and only one God, for example) may not actually be logically contradictory at all. BUT there is another possible consequence that is not so often contemplated and that is that things which we have no reason to see as logically contradictory may actually be so.
When I observe the things that children say, this latter type of consequence becomes quite apparent. Not having learned the limitations of logic they may indeed not see that things are logically contradictory when they are. They may in their immaturity make demands that are impossible to meet for this reason and I am led to wonder how many demands we make of God are like this as well?
Now a related question for the consideration of the religious in particular is this: is there any reason to expect that the correct understanding of what is logically possible as God understands it is something that we can fully comprehend at this time? Assuming for now that scientists are correct about quantum physics, is that something do you think that could have been explained successfully to the followers of Jesus? I don't think so. But if that is the case then the whole and complete truth was beyond their comprehension and therefore we can conclude that what was explained to them was limited by their ability to understand (John 3:12 and Matt 13:10-13).
Furthermore, I would expect that there were things explained to them in this manner: 1+1 = 2 because daddy says so, which means they must take daddy's word for things when the explanations were beyond them. But just because a child cannot understand something doesn't mean that he never will and just because people 2000 years ago could not understand something that does not mean that we cannot understand it now. But what do we say to someone that refuses to go beyond the simple explanation that was given to them as a child or to people that refuse to go beyond the simple explanation of something that was given two thousand years ago? Perhaps we can argue that if it worked for people 2000 years ago then it will work now as well. But the same is true if a person clings to the admonition that they never stick anything into electric sockets. They will still be safe from electricution just as when they were a toddler, but I doubt that we can admire their intellegence for not being willing to get beyond this truth appropriate for toddlers to understand better than this.