My break barrels in .20, .22 and .25 have easily taken both raccoons and woodchucks out to the 30 yards or so I have to shoot in so yes, it can be done. Between the eyes or between the eye and ear has taken every one of them I've ever laid crosshairs on.
Recoil, which you asked to have be minimal, is where the sticky part comes in because a springer, regardless of caliber has it. Shooting one and accurately takes practice. There's also 35-45 pounds effort needed to cock one, so also something to take into account and maybe why Jerry said a break barrel was not the correct tool??
The only way you're getting a minimal or no recoiling air rifle is CO2 or a PCP.