Well, I’m really the wrong person to ask if you’re looking for the opinion of a Christian. But most of the accounts I’ve heard and read from other Christians tend to rely on some sort of a posteriori evidence, be it an external event they’re convinced was caused by God, or just the sensation of His presence (I’m calling this a posteriori because these folks have the phenomenological experience of some external force acting upon them, regardless of whether or not that is actually what’s going on).
On the other hand, maybe claims like, “I was lost until I found God” could be taken to be a priori, because it could mean that these particular individuals found within themselves, entirely through self-reflection, that lack which could only be mitigated by a divine presence. But then again, saying that you’re unfulfilled without God doesn’t imply the existence of God—it could just as easily mean that you’re doomed to be permanently unfulfilled. There’s another step somewhere in there.
So I don’t really know. The only truly a priori argument I can think of for the existence of God—in the Kantian sense, unless I’m mistaken, though this predates Kant—is Descarte’s proof. But Descarte’s proof is a total mess, and I wouldn’t encourage anyone to emulate it.
I guess I’ll open this up to the believers in my readership. Not just the Christians, but anyone who places faith in the divine. Are you basing that faith off of external evidence, personal reflection, or some combination of the two?