Do you have access to where the pigeons are in your area (your barn, a neighbor's)? If you want to catch them on the cheap, I use a simple fish landing net -- the bigger the better -- on the end of a long (really long) poll or section of PVC pipe. I take the kids out at night to where they roost (the pigeons that is, the kids roost in their beds!) and have the kids shine a flashlight on the birds while i hold the net up to them and when they take off I net them. It is fairly easy because the birds are basically blinded by the light. It is harder in silos but I have caught them there as well. As a kid I 'd quietly climb up the inside of silo and use the light only as I needed it. They sometimes roost in a cupola (that funny structure on some barns for ventilation) if you can access the insides of one from inside the barn.
As far as feed, the wild ones are very resourceful and I feed them what the cows or horses eat, but they like to pick through mixed bird seed. DON'T feed them raw soybeans because it can be toxic to them. They love corn, also. a little small grit is also necessary if you keep them.
The best time to get them to stay around is to pen them up long enough for them to nest. that mother instinct is strongest and the birds will stay if they have young to tend. Anyway, I hope that gives you some ideas.
