These are questions I would work up to or start with depending on who I was talking to. Something for Catholics, Protestants, unconventional theists, and their intersections:
"What do you find to be the strongest argument against metaphysical reasoning, especially of the sort that suggests the concept of God as a compelling foundation for metaphysics?"
"Does your philosophical conception of God intersect with decisions in your day-to-day life, or during critical periods in your life? If so, how so?"
"Most analytics are two-boxers on Newcomb's problem, but William Lane Craig makes a case for one-boxing; what do you think of his arguments? What do you think of his approach to the problem of Divine Foreknowledge, e.g. as compared to Thomists and Molinists?"
"Many mathematicians that thought about infinity and the divine ended up with baffled and baffling impressions; e.g., Cantor, Goedel. Do you see this in philosophy? Do you have any thoughts on what it implies about the concept of God and how you should go about reasoning about God?"
"Do you ever try to find room for theology in your phenomenology? If so what does that look like? Can God be examined phenomenologically? If so, how?"
"Would the idea of God be a necessary or at least highly compelling idea to hold just because of its theurgic effect, so to speak, on society and on individual philosophers? E.g., as a bastion against relative anomie and nihilism. If so, is that evidence for the justification of its philosophical underpinnings, and if so, what is the mechanism of justification? [Maybe make a reference to Plantinga's arguments against naturalism.]"
The point is setting up a conversation where you both feel like you're learning or sharing important but nuanced ideas.
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.