Two words.... PIT BULLS....
I doubt pit bulls would do much with the Eastern Coyote except for providing a lunch. Only dogs that will work are livestock guarding dogs (multiples thereof with spiked collars). Eastern coyotes can weigh about 50 lbs so several territorial dogs that are much larger are needed - Maremmas or Akbash or other mastiff derived breeds.
Coyotes don't interbreed with dogs. Dogs cannot survive in the wild because they have pups at all times of the year.
The old "coy-dog" label was never true.
The coyotes were interbreeding with wolves.
Many of our neighbors keep donkeys with their cows. Works like a charm.