My answer's simple: miracles. However, I make sure to specify that they can't just tell me this one amazing story of a prayer coming true to a cousin's friend of theirs. If they can provide evidence of "million-to-one" coincidences happening more often than 1/1,000,000 times to people who prayed for that event to happen, I will revise my probability estimate of God upwards. Bayes Theorem 101. If we could see that prayer works consistently, or at least works better than chance, a rationalist would start praying.
But wouldn't that just provide evidence that something, somewhere is bringing about something we though was impossible via a petition?
In other words, even if that happened, I might still not believe in the god under discussion. Indeed, in the past I've said that an amputee regrowing their limb in front of me at a request in the name of Jesus and initiated by a hand clap or the command, "Now," would work. I now think this is incorrect.
I say this because even if that happened... what about all the other stuff I find incomprehensible, dubious, outri...
I have a feeling that most of the people reading this site already understand everything in this article, but it's a useful synopsis of common issues faced when trying to have a reasonable discussion with laypeople, and might be good to point them to if necessary.
http://thoughtcatalog.com/2011/how-to-have-a-rational-discussion/
I also want to mention how much I wish someone had shown me something like this as a teenager- I was very prone to lecture others against their will- as it might have saved me a lot of grief. I'm curious to see if these tendencies might have been common among members of this community growing up, so please comment to tell me if so (actually, please tell me even if not-no reason to encourage my own confirmation bias)!