As I recall, our own Matt Bracken once gave a fairly effective solution a while back that could be summed up in two words:
Nuke Mecca.
One of the ‘major claims’ of Islam is that “Allah” will never allow harm to come to Mecca. The Muslims firmly believe that Mecca will never be destroyed.
He postulated that if you destroy Mecca, Muslims would be disheartened (at the very least) to know that the claims of their “Allah” turned out to be false. Granted, it might spark a massive ‘holy war’ by Muslims worldwide, and we’d have to be prepared for that.
At some point, we're probably going to have to deal with that, anyway.