I don't care what bullet you hit a Grouse with. Solid, cast HP.. You're going to have more damage than you want. With centerfire on Grouse, You're best to shoot the base of the neck and/or head off. To do that, you want the most accurate, (doesn't matter what kind), of bullet your gun/you shoots.
Bird shot from a 9mm has more velocity than you'll get from a 38spl revolver. Bird shot affect from 38spl is dismal at best. Best left to snakes at very close range.
-Steve