You can train your chooks to go thru pop door cover made of strips of clear plastic that the smaller birds can't get thru.
If your coop is attached to a run, you can cover the run with bird netting.
Your location and coop/run configuration would help folks make suggestions.
I have trouble with cardinals~and like you, it's like the movie BIRDS. First the baby goats were going in the door, fixed it, and now the birds! I like the post about the plastic strips on the door. I am going to try it.
I've never had large numbers of birds in the coop, but one time I had a sparrow, and I spent 10 minutes chasing it around until I finally got it out the main door. I was very pleased to have freed the little bird. It flew about 30 feet from the coop, and was about 5 feet off the ground when one of my barn cats jumped up and snagged it right out of the air. I guess it wasn't that birds day!