Judythe, here in the Great Basin we still have a few sheep operators running bands (a band is 1,000+) of sheep out on public grazing leases, where coyotes are a huge problem.

Most operators run one or more of the following types of guard dogs:

Great Pyrenees, Akbash, Maremma, Kuvasz.

The Pyrs and Akbash (or a cross between the two) are the most common.

The Kuvasz is the hardest of the bunch.

Both the Pyr and the Kuvasz can absolutely manhandle a coyote, and take on a wolf when one-on-one. They take on mountain lions as well out here.

To use them effectively as guard dogs with sheep, they need to be "bonded" to the sheep. To do this, you take a weaned puppy and place them with the sheep. You minimize human contact with the dog except to feed it. The result is that the dog becomes "one of the crowd" from the sheeps' perspective, and the dog views the sheep as "theirs." Coyotes are treated rather harshly by these guard dogs; I've seen a male Pyr (about 130 lbs, 30" at the shoulder) shake a coyote so hard that the coyote's neck snapped.

Now the downside: these dogs will be a problem for human interlopers as well. If you have idiotic neighbors that treat your land as their land, or idiot trespassers of any stripe, you may have a liability. The problem isn't just that these are big dogs. There are plenty of "big" dogs out there. All of these livestock guarding dogs are "hard" -- ie, they know their job, it has been bred into them for a thousand years or more, and they could pretty much care less about your opinion. Dogs like a Rottweiler or German Shepard aren't really "guard" dogs -- they were livestock herding dogs that were trained to be guard dogs. The Pyr's, Kuvasz, Akbash - they've been bred for a thousand years to guard livestock without humans around. So they don't care if you're yelling at them to not attack the neighbor's dog that got into your field, or the neighbor himself.