Don't use airsoft. Ever. Period.
.177 cal pellet under 500 fps is not sufficient for anything larger than a field mouse or small birds.
.22 cal pellet (heavy weight hunting round, don't be stupid and use a wadcutter or something) under 500 fps can kill squirrels or small rabbits. Like hunting anything else, shot placement is important: EDUCATE YOURSELF BEFORE YOU DO IT. Don't do headshots with low power air guns, skulls are harder than you might think.
Otherwise use a knife or a shovel (spade) or snap its neck. Don't just let it suffer to death.