As far as I can tell, the feral pigeon has no positive attributes; an opinion shared by all the farmers and ranchers I know. Ask any of them and they'll tell you the pigeon's sole purpose in life is to eat as much grain as possible, convert said grain into poop, and then deposit it on machinery, barns, cattle feed and anyplace else where it's not welcome. No wonder they want them shot.
Enter the pigeon hunter. Although these birds can be hunted at any time of year, I usually don't get around to busting pigeons until fall. It just seems to fit into my schedule at this time of year, and as long as I hunt around the barns and corrals before the cattle come back in from summer pastures (around the middle of October) I'm welcome to shoot just about anywhere.
Around here, any farmer with an open building and some grain has pigeons, with the typical farmyard hosting a flock of 20-30 birds. Pigeons can be hunted at any time of the day, one method being to stalk around buildings and corrals with a quality pellet rifle or a 22 rim-fire loaded with CB ammo. This is fun, challenging and a good way to hunt if there is excitable livestock in the immediate area. Low powered guns and ammo also allow the hunter to shoot without penetrating walls and make missing an shot at a pigeon less of a concern.
Another method is to grab a shotgun, locate the building in which the pigeons are roosting for the night and identify the opening(s) through which they enter and exit. About thirty minutes before sunset, sneak into position next to these openings and make enough noise to convince some to fly out. At your first shot, the barn/shed will empty in an explosion of pigeons and for twenty seconds you'll be offered a target rich environment. This is where a semi-auto with an extended magazine is the perfect tool,because if you have to reload the birds will be gone by the time you're done. This is why my Remington Versa Max Tactical got the nod for pigeon duty last week. With my challenge being to see how many birds I could drop with one full loading of the gun. My score was five, proving once again that I'm not a great wing shot. However, the shooting isn't necessarily over, sunset pressures the birds to return for the night. Often, sitting tight and hiding will result in few more downed birds when they come back.
Some people eat pigeons and I've heard they're tasty. Personally, I can't do it; likely because of that rats-with-wings label I've given them. Besides, the farm cats always enjoy seeing me show up. They eat rats.