Concerning getting guard dogs, unless its a very large breed, you need two dogs, coyotes can pack and will gang up on a single dog. A male and a female pair is prefered, males will occasionally fall for a female coyote in heat, and get lured to his demise, won't happen if theres a girl with him.
I have seen several neighbors loose dogs to coyotes.
The other thing is coyotes are a highly intelligent and adaptable animal ( thats why they are in Florida, New Jersey and other non native habitat ) so they can and will act differently in different parts of the country. They are true survivors and just amaze me how they can adapt to differnent biospheres.
If your trying to hunt them a wounded rabbit call is very effective ( if you don't know how to use it buy a tape ), even better is a spoiled dead rabbit with the call. If you have access to a spot light ( like on a 4 wheeler truck or a old cop car ) thats even better. I never had much luck with a shotgun as they are very wary and I prefer a .223 or there abouts to hunt them.
Heres a couple of quotes from Wikipedia:
" At one location in Southern California, coyotes began relying on a colony of feral cats as a food source. Over time, the coyotes killed most of the cats, and then continued to eat the cat food placed daily at the colony site by citizens who were maintaining the cat colony.[59] Coyotes attack smaller or similar sized dogs, and they have been known to attack even large, powerful breeds like the Rottweiler in exceptional cases.[73] Dogs larger than coyotes are generally able to drive them off, and have been known to kill coyotes. Smaller breeds are more likely to suffer injury or death."
" Coyotes typically grow to up to 3034 in (7686 cm) in length, not counting a tail of 1216 in (3041 cm), stand about 2326 in (5866 cm) at the shoulder and, on average, weigh from 1546 lb (6.821 kg) .[5][13] Northern coyotes are typically larger than southern subspecies, with the largest coyotes on record weighing 74¾ pounds (33.7 kg) and measuring over five feet in total length"
"Though coyotes have been observed to travel in large groups, they primarily hunt in pairs. Typical packs consist of six closely related adults, yearlings and young. Coyote packs are generally smaller than wolf packs and associations between individuals are less stable,[20] thus making their social behavior more in line with that of the dingo"
The other hard part about them is the range they cover, its over 10 miles from their burrows and nests.
Coyotes are a tough preditor, and where there is one there are more thats for sure.
Their natural preditors are Mt Lions and Wolves but I doubt thats going to help unless you want one of them to guard your coop: