I hope it's alright that a non-believer is posting here, but I happened to see this topic and, as someone who has been an atheist essentially since I was about your son's age, I thought I might be able to give you a useful perspective.
[quote="bernadet, post:1, topic:232516"]
My son has asked me if I can prove God exists, but I don't know how to explain this in a way that is both persuasive and age appropriate (he's not going to get it if I talk about St. Thomas Aquinas).
Well, in the first place, I think a lot of religious folks would admit up front that proving the existence of god is indeed impossible -- that's precisely why religions say that faith is necessary. After all, if you could conclusively demonstrate that your god exists, you wouldn't need faith to believe...you'd have solid evidence, not faith.
And there's the whole problem. Your son will probably next ask why you should have faith at all and/or how you use faith to determine that your particular god -- the Christian god -- is true, rather than all the hundreds of other gods proposed by religions. And you won't have a good answer for that question because there's not one. Trust me, I've been at this for a long time, and I'm familiar with all of the arguments and angles, and there simply is not a convincing argument. If you want to convince your son honestly, you probably aren't going to do it through argumentation.
I would recommend that you try one of two things:
1) Explain to your son the things that convince you that god exists and ask him whether he also thinks that they are convincing. If he doesn't find them convincing, ask him why not. This will at least open up a dialogue, which could be very fruitful.
Option (1) will require you to think about what convinces you of the truth of your religion. Unfortunately, as I indicated above, I don't think that there are any convincing arguments -- at least, no convincing arguments that do not require faith to bolster them. So perhaps your best option is to combine option (1) with the next option:
2) Pray to your god to reveal himself to your son. After all, if your god does exist and if your god is all-knowing, then he already knows exactly what would convince your son to believe in him. So ask him to present your son with whatever it would take to get your son to believe.
It sounds like you are approaching this issue in the correct manner, giving your son a lot of respect, and that you're willing to be intellectually honest with him, which is great.
I'd be happy to answer any other, more specific questions, but if not, good luck with everything.