They say ".22 for fur, .177 for feather" in reference to the smaller caliber air rifles. I have taken dozens of rats and chipmunks with a German-made Diana Model 34 in .177 with red dot scope mounted. The double "whack" of the piston as it rebounds can play havoc on lesser quality scopes. More damage than a traditional rifle because the initial slight push from the release of the piston is reversed as the piston stops abruptly. Scopes specifically made for air rifles tend to have crosshairs etched into the optical glass. My red dot does just fine at the limited ranges I shoot. They're fun and can be used in your home with a proper backstop or ballistic putty backer. They can keep you in your shooting hobby right through the snows, as well.
"Wars are, of course, as a rule to be avoided; but they are far better than certain kinds of peace." - T.R.