Need something to knock down a few squirrels making residence in my attic.
In city limits. BB. Pellet.

Better to trap....bait with peanut butter.

That worked best when we had squirrels in the attic. Suckers were hard to find with any type of weapon.

We had same issue of squirrels making a home in the attic, right above our master bedroom. I bought 2 varmint traps, and trapped about 4-5 of them with peanut butter. I placed the trap right outside their entrance on the roof (I had easy access to get on the roof) But I ended up shooting 8-10 of them with a 22 using 22 shorts. They are much quieter, and pack enough punch to go in and not come out. I tried 2 BB guns and a powerful pellet gun, and even the pellet gun would not kill them with multiple hits on them. 22 shorts out of a Win lever rifle was the answer. I would only take the shots that were 100% (i.e.- where I knew I would not miss) and in a safe direction with a solid back stop, often times a tree or my fence (from an angle). I would snipe them from inside shooting out, often times at the base of my back yard tree. I would open the window and shoot through the screen. I shot through the screen in the same spot in the corner of the screen in an area where you could not see it. So, it was a pretty cool set up or sniping spot. Once I killed a lot of them and trapped the rest, we were good. I still hate squirrels for this reason.

Some cities have an ordinance banning air rifles, check first.

I have used wrist rockets with ball bearings...... They drop like a rock.
Takes practice, but worth it. Practice with cheap marbles, then switch to ball bearings about marble size.