i do it with an air rifle, i use the crosman phantom, it goes just under 500fps, get a scope, hit em in the head.........other wise its like using bird shot on a wild turkey!
if you head shot em they go down easy.....other wise anything beyond 20m or so, wont have the punch to kill it properly and quick....im my opinion.
make sure you have your hunting license too, you need a small game tag for crows last i checked.
for the price of an air gun, why not pick up a used 22 and some crow decoys.....set one in a tree like a lookout.....a couple more on the ground........a half loaf of bread......and they will come in.
cheers