As far as trying to come up with a logical argument why said supernatural CANT exist - It cant be done.
You would be trying to prove a negative. The goal posts can always be moved to leave room for the possibility.
The most famous example is Russels celestial teapot. http://en.wikipedia.org/wiki/Russell's_teapot.
The point is it is not for the non- believer to prove there is no god, it is the believers responsibility to present the evidence that there IS a god(s). That evidence either convinces you or it dose not. As a non-believer, I remain to be convinced. But thats to say I couldn't be convinced, its just that all the arguments and "evidence" for a god fail on some some level.
