I use a crosman 1322 (the 1377 in .22cal) pellet pistol for grouse while im out hunting deer, drops em on the spot most times.
Ive killed many magpies with cheap Chinese .117 pellet guns that shot under 500fps and even with .117 zinc bbs out of a daisy repeater. Its more about shot placement and the kind of pellet you use I find.(Just like a real rifle different air rifles like different ammunition so experiment.)
I use hollow points on pests for maximum expansion.