The trouble with questions like these, I think, is that the answers of elite theist philosophers, in the first step, are most likely to be the same as the answers of much less capable theist philosophers. The points where their answers are more likely to differ are a few steps down the chain of challenge and justification.
In my experience (and by the description of Luke Muehlhauser, whose experience is probably quite a bit more extensive than mine,) philosophers of religion generally know a series of several standard challenges and answers, which have been hammered out in philosophical debate over decades to centuries, in much the way that expert chess players are familiar with a wide variety of openings and gambits. A chess grandmaster isn't going to be distinguished from a regular expert by knowing some awesome esoteric opening, but by their knowledge of how to follow up in the rest of the game which makes the opening better worth using.
Yeah. I should think about how to get around this, and glean useful information from their expertise.
I am about to graduate from one of the only universities in the world that has a high concentration of high-caliber analytic philosophers who are theists. (Specifically, the University of Notre Dame, IN) So as not to miss this once-in-a-lifetime opportunity, I have sent out emails asking many of them if they would like to meet and discuss their theism with me. Several of them have responded already in the affirmative; fingers crossed for the rest. I'm really looking forward to this because these people are really smart, and have spent a lot of time thinking about this, so I expect them to have interesting and insightful things to say.
Do you have suggestions for questions I could ask them? My main question will of course be "Why do you believe in God?" and variants thereof, but it would be nice if I could say e.g. "How do you avoid the problem of X which is a major argument against theism?"
Questions I've already thought of:
1-Why do you believe in God?
2-What are the main arguments in favor of theism, in your opinion?
3-What about the problem of evil? What about objective morality: how do you make sense of it, and if you don't, then how do you justify God?
4-What about divine hiddenness? Why doesn't God make himself more easily known to us? For example, he could regularly send angels to deliver philosophical proofs on stone tablets to doubters.
5-How do you explain God's necessary existence? What about the "problem of many Gods," i.e. why can't people say the same thing about a slightly different version of God?
6-In what sense is God the fundamental entity, the uncaused cause, etc.? How do you square this with God's seeming complexity? (he is intelligent, after all) If minds are in fact simple, then how is that supposed to work?
I welcome more articulate reformulations of the above, as well as completely new ideas.