If the coyotes live near cities or suburbs, then we should shoot the coyotes with dart guns and take them to a rural area. Where I live they kill cats all the time. My parents live right in the center of Phoenix metro area and the coyotes come from a federal park right nearby and kill cats every night. It is sick. Stupid liberals prefer it that way. About 20 years ago in LA a coyote came into a back yard and took an infant from it while the parents watched. But fortunately that kid survived as coyote dropped it when dad ran after yelling. But there have been children killed by coyotes. What does it matter? In Idaho they release grizzly bears into the woods knowing full well that people have houses in the woods. In many states they've released wolves or mountain lions. In California two women were eaten by mountain lions released by our federal guv friends. I myself have lost two cats to coyotes.
If the coyotes live near cities or suburbs, then we should shoot the coyotes with dart guns and take them to a rural area. They'll just come back. It would be better to shoot them dead. Coyotes are EVERYWHERE because they are so darned adaptable. They are not only predators, they are scavengers, and will happily dine out of garbage cans. They will munch on little dogs, and seem to just love kitties.
They run in packs, so, while a large dog might scare one off, a pack of them would make short work of even the biggest, baddest pooch. They often use female coyotes as bait to attrack male dogs to eat.
We'll never be rid of them because they thrive on civilization. A lot of guys I know love to hunt them, and, on balance, I think that's a good thing.
That's why I keep my cat inside. He's perfectly happy and I don't have to worry about him.