I too have spent some time in cleaning out (well - reducing) pigeons from barns. (By the way, is it possible for you to do them inside the barn with a pellet gun? That (usually) doesn't do damage to the barn.
And after the initial fun, and the cleaning part, I've done 'em up similar to mt3030, the same way I do grouse.
Breasts with a strip or two of bacon wrapped around and held in with toothpicks. Slice up a sweet onion, a tomato, add a dollop of butter, season as desired (usually just salt and pepper for me) and wrap in tinfoil, put in a baking pan or pyrex tray and bake in the oven.
I pre-heat the oven to 450F, put the pan/tray in and immediately turn the heat down to 250-275F. Let it sit there for a good 30 mins then unwrap the tinfoil, check the meat, (leave it in longer if necessary).
When meat is done (no pink) you can serve and eat immediately or if desired (which I usually do) drip some of the juices over the meat, turn the temp down to 175ish and leave it in the oven another ten minutes or so.
Another possibility (and I often do this with chicken breasts) marinate, preferably for 2 hrs or more (probably more is better with pigeon/grouse etc) in your favorite salad dressing (recently I've been using Sweet Honey Catalina, and Garlic Ranch by Kraft). I just put the breasts in a zip-lock sandwich bag, pour in a healthy dollop of dressing, smoosh it around (I hope no one objects to my using such technical chef jargon!) and then let it sit, turning over the bag and smooshing whenever I remember to do so. Can also be done in a suitable sized bowl covered with plastic wrap or tinfoil.
After the marinating time (in truth that is anywhere from a couple of hours to a couple of days - depending on my memory) I put 'em in the oven as described above (or slap 'em on the barbeque). With the chicken I leave out the dollop of butter and the tomatoes but often add onions and/or mushrooms. And chicken breasts would be thicker so I'd leave them in for at least 45 mins.
*Note: ovens are not created equal, so you may have to experiment a bit re tempuratures and times.
Another way to do a number (6 or more) small breasts (like grouse) is to dip them in a homemade or commercial 'breading mix', fry 'em up in butter (or garlic butter -yum) and as Wally says: "Shoot/eat/repeat" :agree:
Have fun.
Cheers
Kerry