Just in case this is a surprise two things to remember. LGD have no fear. It was bred out of them years ago. Good ones will not give up on their jobs no matter what. Coyotes are not really that big. They all fluff so they look twice as big as they are.
Though LGD should never work alone. There should always be at least two dogs if they are guarding unfenced animals.
Things like Great Pyrenees, Kuchi, most things with "shepherd" in the name, mastiffs. Breeds like that.
Anecdote time: I have a Pyrenees collie mix, and a small terrier. The Pyrenees protects the terrier when they're outside, mostly from the hawks/owls that like to fly around the fields looking for rodents. But I have gone to check on them before and opened the door just in time to see the Pyrenees barking up a storm chasing off a coyote. I'm confident that a coyote wouldn't be able to get through my fence and attack the terrier before I could grab something and fight/scare it off, but I know with the Big Boye out there I don't have to worry about it (but still do, people tell me I Dan leave them out there for longer periods but I keep pacing by the windows and back door to check on them every minute or so they're out there)
I don't think most people realize how small coyotes actually are. Depending on the type, coyotes weigh on average 25-35 pounds, with the largest males not topping 45 pounds. The smallest male Great Pyrenees weigh 100 pounds, and can get up to 160 pounds. Those coyotes didn't stand a chance, didn't matter he was outnumbered 10 to 1. Imagine the average adult male versus ten five-year-olds. They might do a little damage, but they don't stand a chance of winning.
Yeah it is not close to an even fight. I even saw a video once of a Komandor ruining two off wolves. It was an amazing thing to see. Yeah the wolves could have taken the dog but it would have taken one of with it. It came down to the fact that the dog didn't consider being hurt as a problem and the wolves did.
Too often women and men forget that you need to kill and maim when fighting for your life.
The amount of times I've seen people just roll over and die when being attacked by smaller animals because they don't want to fight back or hurt it is too damn high.
I have a Great Pyrenees and couldn't agree more. Not super surprised about killing the coyotes either; my GP is insanely sweet to familiar humans but has a viciousness towards strange animals like I've never seen in another dog before. And those coyotes were probably a 1/4 of its size.
Yeah I used to know a lady who had some Pyrenees to guard her sheep. They would spend all night running the coyotes off. Then come in for breakfast and sleep all day while her 2yo would drive his toy truck over the dogs. They would never even raise an eyebrow at her kid. To them it is all part of the job.