The JREF challenge, linked to via Nancy's post, did not ask for evidence of the existence of God, but for evidence of supernatural power. I misunderstood this when I read her post, but when I followed the link I got it clarified for myself.
It got me to thinking about the existence of God (although I think "existence" is a state that He somehow transcends) and what the evidence is.
I do not think evidence of God is found in the "supernatural" but in the natural.
I find no conflict between science and religion. The study of science and natural laws, the development of the human mind leading to new discoveries, new abilities, new medicines, new treatments, new technology, is the study of God's world.
I find no conflict between the "theories" of creation and evolution. I don't think there could be one without the other.
In fact, in the astounding evolution of the natural world as it is now and as it continues to evolve, I find the greatest evidence of God's power.