Get a terrier. They're little murder machines bred only for slaughter. Alternately, pay one of the neighborhood kids to sit out back with a bb gun and take care of it.

Failing that - Rat traps, or live traps if you're feeling merciful though squirrels are intensely territorial so make sure to drop them at least a few miles away.

Really the only way to get rid of them is to kill or capture faster than they can breed. Even if you remove the ones there now new ones will agressively move in.

Maybe you could take up falconry?