Why do you believe?

[Whateverist]

Here's my point: Naturalism (atheism and materialism, essentially) entails that prayer never works--and when it "does", it's only coincidence.

So if any prayer ever works, you have evidence that disproves atheism.

That depends on why the prayer worked. It might well be that the act of prayer merely coincides with a healthful state of mind. Someone who prays might then experience healing for that reason rather than as a result of supernatural intercession.

I don't see how the occasional coincidence of what is prayed for with what in fact happens could possibly disprove atheism.