I have the Gamo 440 hunter in .177. It's plenty powerful and accurate for squirrels. I bought mine for that exact reason, squirrels. If you can aim it, it will knock them down. My extensive live testing shows that the pointed "hunting" pellets are useless. They don't do enough initial damage. Certain hollowpoints do very ok, but not great. It's hard to beat the flat wadcutter pellets for pure knockdown effect.
I like these:
Found these to be highly ineffective with dropping squirrels immediately:
Avoid these if you want "humane" kills.