Sterilization will not work. What you need to do is to convince muslim women that they have "choice" and that they do not have to keep that parasite alive. Show them Planned Parenthood and their works! Then buy off a few imams with some walkin' 'round money to advertise for PP and watch the birthrate plummet. It worked with another group.
Try going to your local mosque and then interact with the women there and see for yourself the futility of that plan. Muslims in general, and Muslim women in particular, hate the West and are suspicious of Westernerd to the point that they regard them as no better than philandering reprobates deeply indulged in sexual depravity, especially due to their cultural aversion to premarital sex.
In a perfect world, IMNSHO, not a single Muslim would exist. However, the sexual attitudes in the West will ensure that Islam will thrive here.