I don't think autopilot landings are legal, even if they are possible. Autopilot is mainly to keep the plane flying straight and level, as far as I've ever heard.
Automatic landing systems are commonly used in commercial aviation, but don't use GPS (
http://en.m.wikipedia.org/wiki/Autoland).
I'm not a pilot, so if one of the licensed pilots would care to chime in, I'd be glad to learn more n