When I lived in town, I went from a .410 SxS to .22lr hp to .22 short hp, to a .177 air rifle in an attempt to keep some greenie in the in the apartments two lots away from getting upset. I had good success with all, except the air rifle. I was dispatching them as vermin. My 70+ yr next door-neighbor trapped them in a home-made wooden rabbit gum, dumped them into a burlap sack, whacked it hard against a tree, and then cooked them in a crock-pot. He said the young ones were tasty, the old ones, not so.
These days, in the sticks, I thin the squirrel population with a 12 ga Winchester Super-X Model 1, 26" bbl, IC choke. #5 lead high-brass bird. Works every time.
Les