I can't think of any other way than keeping dogs of ample size, power and WILL to take on larger predators, especially in dealing with coyotes. We have a lot of dogs..because we like dogs. In fact, we have a lot more dogs than we need.
You don't have to have a monster sized dog to deal with coyotes but if you're going to have just one dog, the Pyr. would NOT be my choice unless you get it from bonafide working stock and get it no later than 8 weeks of age. AND...don't make it a pet, at least not right off but allow it to grow up in the chicken area, but in a way that it can not harm the birds in it's youth.
There are people on here who know a lot more about standard LGDs than I. for working face-to-face with our chickens, we use a non- traditional breed and we use Larger somewhat dangerous dogs to run at-large during the night when the chickens and other dogs are safely locked up.