I've never heard of using a "dog" to hunt "dog" (coyote) with. I guess it could work, but seeing that probably 99.9% of hunters in American do not use dogs when hunting coyote or bobcat I don't think you'll have any real luck in finding a good working dog.

Yeah, they use beagles on fox in the UK, but a fox is only a little bigger than a house cat (in general). trying to find a dog to go after a big coyote and chasing it for miles, may be tricky.

I'd get hound dogs and go after mt. lions instead. At least the lions will tree up somewhere. I think a coyote would just keep on running for a long long time. NOt worth the hassle in my opinion. I'd just try calling in another coyote somewhere else.