I just received a great airgun, purchased from pyramyd air. They have everything you need for pest control. Ships fast and great customer service. They offer a 10 for $10 service in which they test shoot and chronograph ten test shots to make sure the rifle is up to spec and not a dud. Not sure what your budget is but I got the Hatsan 135 vortex for $229. And couldnt be happier. Great quality rifle. Its powerful in .25 and really packs a punch (ive got bigger problems than squirrels). For squirrels .177 or .22 is more than enough with the right gun. I hear great things about Hatsans 125 sniper (almost same size powerplant as the 135 but with synthetic stock and supposadly a tad quieter) also the 95 vortex looks real nice for your needs. The 135 i have seems real quiet to me but it is my first air gun and have nothing to compare it to. Sounds like an nail gun to my ears. I have a little space around my house but a couple neighbors are pretty close and no one has mentioned the target shooting i am doing in the afternoons (30-60 pellets in a row)
One note is if you put a scope on make sure it is air gun rated as the recoil is two ways and will trash a traditional rifle scope.
Just saw your post about not wanting break barrels sorry. Still check out the site they will have what you need.
Hatsan seem decent I only have touched 1. A under lever "torpedo " ? The other was a pistol ....looked ok,but not for 130$ they where asking.