Grey, I used to use .177 exclusively for small game, and have taken sparrows, starlings, pigeons, red squirrels, grey squirrels, as well as raccoon.
The thing about bird hunting is that their kill zone is quite small. Aim for the base of their wings and you'll hit the lungs. Profile double lung is the best, but a frontal shot from the ground up is also great. Don't bother for the head, as birds move their heads way too fast.
I can't recall ever having to follow up a starling with my .177.
Speed of my pellets is 900 fps shooting domes, exits every time.