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.
You get yourself two coonhounds, and they’ll take down a cougar, let alone coyotes. Good dogs to have around, keeps the yard clear of dangers, well keeps the yard clean of any wild animals, or cats.
One night several years ago in West Tenessee, a friend of mine and I had three Plott hounds (two small females and one male less weighing than 70 pounds) that decided to ignore treeing coons and instead chased and captured a female coyote. They were close to killing it when we arrived, and they likely would have if it weren’t for a .22 to the head.