I wouldn't -- but sometimes you can eat coyote meat. Best would be either well-done grilled, in a stew or make jerky from it.
This is oversimplifying it, but basically the taste of the coyote will reflect what it's been feeding on. Around populated areas, forget it. Coyotes will scavenge garbage and feed on rodents and old carcasses, and that gets into the fat and skin, and you won't tolerate the taste, let alone the smell.
The only time I've heard they're remotely palatable is up north where they may follow a wolf pack and scavenge a lot of fresh meat. or very strong young yotes that can bring down deer and are eating lots of fresh kills like rabbits. Older or feeble yotes won't taste as good. When you get near it to try to skin it, you'll know. I'd say, 99% of the time you'll hold your nose and walk away.