When considering poison baits:
"Suffering bobcats, coyotes, owls spur Thousand Oaks neighborhood to rethink war on rats"
http://www.latimes.com/science/la-me-0206-rats-20160208-story.html
A related quote:
"The insanity of it all is that in trying to wipe out rats they are killing the very animals that keep rat populations under control."
The problem with this story lies in how the anticoagulants work. The animal needs to ingest about 10% of their weight. Birds are extremely !eight, so its possible they could eat enough rodents to vet a lethal dose. But I have a hard time believing this could happen with a bobcat or coyote. You are looking at pounds of it being needed when bait stations hold between 22 and 200 grams each.