Let us assume that a divine being exists. Furthermore, this divine being, in addition to being immaterial and supernatural, is also omnipotent and omniscient.
Any divine being possessing these characteristics could blind any non-divine being as to the existence of the divine being, and, if they wished, could make it appear that they never existed. Therefore, it is impossible for any non-divine being to prove the nonexistence of a divine being.
"Ah!" but the sceptic says. "If it is impossible for me to disprove a divine being, it is equally impossible for you to prove one."
Not so. The reason that a divine being can't be disproved is that the possibility of the prescence of a divine being brings any natural processes into question. If we start from the assumption that there is no divine being, then there is no supernatural to confuse the natural.
This reason doesn't prove a divine being, any more than it disproves one. All it does is disprove the disprovability of a divine being.
In summary: A divine being could hide itself, so we can't say there isn't one.
^ ^ ^ That's what I thought of while practicing violin today. It doesn't take into account why a divine being would want to hide their existence, but I didn't think it was necessary in order to make my argument clear.
Any critiques? Thoughts? Feel free to play devil's advocate :)