The secret is to introduce lions to feed on the coyotes. Think of the tourists coming to San Francisco to watch a lion kill and eat a coyote. Why, it’s almost like Jurassic Park!
We've got a lot of coyotes around here. Many nights if I walk out the back door I can hear them yipping outside of town.
Ironically, in the context of your post, we're getting an increased number of mountain lion sightings hereabouts. Just had a guy tell me that one of the deer hunters nearby caught one on his trail cam. And quite a few farmers, including my uncle, have reported seeing them all over the place in western Iowa.