The documentaries that New Atheists make probably. I would definately not count Contact (though I did like that movie, especially the 'mood of the world'-scenes), since the message is basically that atheists need to get of their high horse and open their minds.
The problem with making an 'atheist story' is the same reason why I don't buy into the New Atheist idea that God can be disproven: It is physically impossible. One can never scientifically prove that anything does not exist. You can do tests and say how and where you looked, but that doesn't prove it isn't there, just that it can't be found the way you describe it. And when we get to an almighty god, there is not a single thing a human can do that could prove his non-existence. He's almighty, so no rules apply to him. If your experiment doesn't find evidence, all the believers need to say is that god doesn't want to be found by this experiment. There's no way to disprove that.
In movies, this translates into the difference that a Christian movie can just show a demon, an angel, or a miracle and that makes it a movie that shows Christianity as correct. An atheist movie... can NOT show a demon, angel or miracle, but that doesn't exactly demonstrate those things don't exist. Most people don't see supernatural entities in their own life either, and many don't consider this proof they aren't real. You can perhaps make a movie that displays one particular bit of religious dogma is wrong, but odds are there are plenty of other religions that don't believe in that bit of dogma either. I haven't seen Paul, but it sounds like that's what it's doing: Giving an anti-creationism message, but not all of Christianity denies evolution, nor do some other religions.
So by construction, it's very hard to make an atheist-affirming movie, and if you do it's bound to be as obnoxious as the worst of the religious-affirming movies. Not because the atheist message is wrong, but because any belief that something exist can be confirmed in a movie by showing that thing. Not showing the same thing in your movie on the other hand, does not prove that it doesn't exist, and you're going to have your characters just brazenly claim it doesn't exist all the time. That doesn't make for a very interesting movie.
