Are the pigeons just loafing at random points, or do they seem to be using specific areas for nesting/roosting? I have done some pigeon trapping programs with varying success, but in most cases can solve the problem using exclusion measures at the "attraction" points. If you can take away their access to the nest/roost sites, they will quickly move to another location.
Did this one up at a large Ford truck dealership.... they had 2 other companies try trapping over a 3 year period, but never had any lasting results. After installing $50,000 in new AC units, their HVAC service company found the new units packed with pigeon nests within 3 months. We all know that is about 14 sticks and 2 pounds of poop per nest. The HVAC company warned them that the new AC units would be toast in no time if the pigeon issue wasn't dealt with, and I was the one the AC company told them to call.
I built a framework using metal conduit. The existing enclosure for the AC units provided a perfect support system. Standard cable support system with turnbuckles and then a translucent 1.5" bird netting was installed. The lower edge needed sealed, but had to allow for ventilation, so I used 1/2" hardware mesh and secured it with metal tabs and self-tapping screws.
After spending a bunch of money on trapping programs and every other gimmick the pest control guys could find to sell them, the pigeon problem was completely solved by the installation of this netting. There were about 100 pigeons using this site, and they have now moved about 1/2 mile down the road to a gas station canopy. Maybe I'll get to deal with them again!
Here's a few pics showing the enclosure. I made an access door using PVC pipe for a frame. It sits in 4 "u"-shaped hooks and is secured using two small bungee cords. Really works great... the HVAC guys have easy access into the enclosure and can work standing up, as I made the "ceiling" about 6.5 feet high. Not sure if you could solve the pigeon problem at your site using this type of system, but thought I would share this info.