Great Pyrenes will fuck coyotes up. I know a guy that had one that would run coyotes down on the regular and kill them and carry them back to his farm, apparently to show off.
Knew a farmer/rancher a few years ago who raised both cattle and elk and every spring the coyotes would be a problem. Got himself a couple Japanese Akitas. End of the coyote problem. Beautiful dogs and very friendly with people but not coyotes.
I had several Great Pyrenees and a couple GP crossed with Airedale terroirs, I preferred the cross's as they had no health issues as well as shorter hair.