When shooting pigeons or anything else for that matter, 99% of the time i go for the head shot. This results in an instant, clean kill. Sometimes however that shot isn't possible. If you can, try shooting the bird from behind and between its legs. the pellet will penetrate through vital organs and should bring the bird down neatly.
Also, just in case, have your rifle checked over a chrono for power. Pellets shouldn't be bouncing off birds ever, unless you're using a pistol, which you shouldn't be. I'm currently using a Logun S16s and its shooting clean through rabbits!
PS Pigeons have a breast plate, toughest part of the bird so don't waste time shooting it there either!

What is your main interest. Vermin control/General hunting