It comes up a lot: "What would convince you?" they ask, "that God exists?"
Well, nothing, at least nothing short of a lobotomy.
I'm convinced only by natural reasons: by the evidence of my senses and the workings of my own mind. By definition, I cannot be convinced of the supernatural: that which is, by definition, unavailable to my senses and mind.
If a God were to exist, if such an omnipotent, omniscient, omnibenevolent being who thought it good — indeed the highest good — that I believe that it existed, then I would simply believe. It would be absolutely impossible to honestly doubt such a being, just as I cannot honestly doubt the existence of objective, physical reality (no matter how much I study philosophy). Either no God exists, or God just doesn't give a shit whether or not we believe it exists.
Religion is nothing more than a big con job, there to persuade you to obedience. To persuade you, at the end of the day, to kill the "evildoers" when they threaten the luxury and livelihood of parasitic priests. Nothing more.