Chicken wire, or similar, is going to be your best bet.

My parents had pigeons in their barn for years. They built nests up in the eaves, and made a mess out of everything. All three of us boys had BB guns and were given free reign of killing them. We then moved on to shotguns once we were a little older, but we couldn't keep up.

Stretching chicken wire across all of their nesting areas has cut down on the pigeons even coming around, to the point that there aren't any nests now. We still go over with shotguns every once in a while to remind the little bastards why they don't want to live in the sheds or hay stacks.