A coyote attacked a Golden Retriever here in SOUTHEASTERN Michigan last year. It was being walked on a leash with it's owner... Don't ASSUME they won't snatch your dog. Also do NOT drop your leash. Your dog is not likely to catch it and once out of YOUR sight there will be others and they WILL kill your dog and eat it.
In areas where WILDlife frequents then REAL breeds of dogs are required: Airedales, Pit Bulls, Bull Terriers, Am Staffs, Ridgebacks and other highly combative, high drive breeds. They'd kill a coyote. But I still wouldn't release one to "run one down". If you have two such dogs with heavy collars then have at it I guess but it's always best to avoid the conflict. A well placed round into the 'yote will send his wily rear end to Allah, Aton, whatever name you call your Creator.
"Necessity is the plea of every infringement of human freedom. It is the argument of tyrants, it is the creed of slaves." ~ William Pitt, 1783