You somehow need to get more hawks. Besides Red-tailed Hawks, Cooper's can prey on rats. One of my children saw that. At that time we had a squirrel whirly-gig with corn on it, to lure a squirrel from the bird feeders. The squirrel moved on (They don't last long out here in the open), but a rat would be seen on it now and again. This child was looking out the window when he saw a Cooper's fly in and snag the rat. That is what I call a rat trap!
After asking around, more experienced birders say that typically the younger Cooper's are not agile enough to go after fast birds, so will take easier prey early on. That really improved my opinion of them. I figured it wasn't a big deal if they ate the occasional Junco as well deserved payment for any rats they take.
I had a long paragraph about feral cats, but deleted it.
I am so thrilled
@beckygardener that you do not use poison. We stopped for the very same reason. Ugh... I just remembered that the rat and mouse poison did not get taken to the hazardous waste drop off with other things we do not use any more.
