Door-to-door evangelists nowadays don't even bother trying to prove to you that God exists anymore. Usually they use scare tactics along the lines of "Some day you will be judged by God. Wouldn't it be horrible if you had to tell Him when that time comes that all your life you never acknowledged His existence?" Even if you explain to them that because you do not believe in God in the first place, you feel no sense of insecurity when that event, which has a probability of occurrence of 0, is presented to you, they will continue along that line of persuasion to get you to go to their church, accept their little handouts, or worse of all, let them into your home.
I'm convinced that it is absolutely impossible for an atheist to genuinely change his belief about the existence of God. This is because there really are only two possible ways to convince someone of God's existence, and neither works as intended. The first method has already been described above. It is some variation of Pascal's wager. But if the atheist were to give into that argument, how can he justify not giving into Pascal's wager type arguments of any other kind? I should be able to go up to such a person, tell him that if he killed himself, I would resurrect him from the dead and make him n dollars richer (where n is whatever number is required to offset the small probability that I would actually be capable of doing this), and rest assured that that argument is more lethal than an AK-47.
The other way to convince an atheist would be to make him witness some kind of supernatural miracle as evidence of God's existence. Even though it would be impressive if such a miracle were actually produced, it would still have no persuasive power. For what is preventing the atheist from drawing the conclusion that it was not actually God who produced this, but rather Hod, or Iod, or Jod, or any other possible fabrication that would be sufficient to explain the phenomenon? Since there are no laws whatsoever correlating kinds of miracles with kinds of gods, the atheist is completely justified if after seeing this he goes off and starts his own cult.
In the end, the factor that will make either of the above methods work is the degree of establishment Christianity has in society. The Pascal's wager argument works on the atheist when applied to God only if the atheist assigns a non-zero (although very small) probability of God's existence and absolute zero probability to all other jerrymandered beliefs. The miracle will serve as evidence of God's existence, and not Hod's or Iod's or Jod's existence, only because all the believers claim that it is a work of their God. So essentially both boil down to bandwagon arguments. The atheist, if he decides to believe in God, is not putting faith in God, but rather in the people who already believe in God. So when the evangelists say "Don't believe me, ask God yourself," they should realize that it is simultaneously an impossible, ridiculous, cliched, and comical sell-line.
It is possible for an atheist to change his beliefs about God. But this change cannot be genuine in that it will never be free of pragmatic selfishness. It is always motivated by social pressure, the "just in case" variety peace of mind, a need to identify oneself with an established and respected presence, etc.