Be careful. It's very rare to find an open-minded atheist who is truly willing to listen to and contemplate on the arguments and evidence for God, and you need be careful you're not getting sucked into a debate where he just wants to try and browbeat your faith out of you. I've encountered plenty of those kinds of atheists on the internet, and their primary tools are ignorance and ridicule.
But logically proving God's existence is a big question that's a lot easier to ask than it is to answer (and I suspect he knows that). It's not unanswerable, but the answer can be fairly complex and takes a lot of explanation. Dr. William Lain Craig wrote a whole essay about it which I recommend titled
The New Atheism and Five Arguments For God. In this essay, Craig presents five logically sound arguments for God's existence, but the explanations to support each argument are quite lengthy and complex (although Craig does an excellent job making them understandable).
I point this out only because if your atheist friend is expecting a quick and easy answer then he's going to be disappointed, and I doubt he will have any interest in digging through a piece like Craig's. Perhaps I'm wrong, and he is genuinely interested in finding answers. I've been debating theology on the internet for almost two-decades, so I admit that I'm probably a bit jaded, but in my experience, most atheists just want to keep asking questions until they stump you or you can't answer to their satisfaction, and then they declare victory. They rarely want answers, just more excuses to continue disbelieving ("Ha! That Christian couldn't answer my question, so my disbelief in God is justified!").
Theological debate, especially on the internet, can be a pretty rough business, so you want to be prepared.