Our dogs - a Russell terrier and a Mountain cur/Catahoula cross - do not appear to dissuade coyote activity at our place, except within the confines of the fenced yard. And we hear coyotes nightly. One picked up my chicken and trotted off just a few weeks ago at 10 in the morning.
Had the donkeys not been penned for breakfast, they would’ve murdered that coyote. They are hell on canids. I once looked out the window to see the horses grazing, but the donkeys on red alert. A stray Labrador was snaking through the pasture, eyes on the chicken pen. The donkeys waited until he was good and close, then charged and ran that sucker through 20 full acres of pasture before he slipped under the fence and disappeared.
So…I vote for donkeys. Get two - they like their own kind and they are hardy and cheap to feed. (And also hilarious.) Ours have never bothered the cats. Occasionally I’ll see one pin its ears at a cat, and the cat simply scoots along out of the way.