Pigeons are much larger than your regular songbirds. Rig up a top for the (open) feeder out of windowscreen that is just a little too short for the pigeons to land under/fit under. Smaller birds won't have a problem getting in and enjoying the seed.

And with regards to the fat pigeon who is not afraid of you, temporarily rig up a sprinkler nearby with the on/off somewhere you can reach it easily near your door. As soon as he shows up, hit him with the sprinkler until he leaves. Might have to do it several times in a row because he will keep testing you, but eventually, he will figure that it is too much effort to get a small meal. Don't keep your feeder full during this time, only a little seed, because when your sprinkler blasts the feeder you will ruin the seed for the other birds.

Pigeons are much larger than your regular songbirds. Rig up a top for the (open) feeder out of windowscreen that is just a little too short for the pigeons to land under/fit under. Smaller birds won't have a problem getting in and enjoying the seed.