All we have to do is let nature take its own course where we can, inundate them with "sins" of Christianity and temptations of western civilization, not to speak of freedom to speak and worship.
What's blatantly obvious is that all the extreme Islamic countries are extremely backward and inimical to modernism. One reason why Turkey is not (as) backward as other countries predominantly Muslim in population is because it is a secular Muslim state.
So, while we may not convince them that Islam is wrong, we can show them something that is closer to them in their hearts. And, in time, and some gentle arm twisting, the seed of doubt and the virus of being able to do what one really likes will do the rest.
This all sounds great, but if the "moderates" do not take control and the "radicals" keep killing children in Israel, flying airplanes into buildings and blowing up discos in SE Asia, the world will grow a bit weary of coddling them.
Just keep in mind: Al Queda (sp) did 911, the US invaded 2 countries, killed thousands of the enemy, destroyed their radical infrastructure, chased their "leader" Osammi into hiding in a cave and reset their entire governments. Americans are generally a peaceful lot, but when our comfortable life style is threatened we have a history of getting a bit nasty, just ask the Japanese.