Just want to throw my two cents in . . . and share 20+ years of experience with sighthounds.
Sighthounds (which include Irish Wolfhounds, Borzoi (Russian Wolfhounds), Deerhounds, Whippets, Rhodesian Ridgebacks, Salukis, Basenjis, and Greyhounds) are bred to hunt by sight. This means any movement they interpret as prey will be chased. This characteristic is used in lure coursing where the dogs eagerly pursue white plastic garbage bags tied to a cord pulled by a flywheel & car battery. Sometimes, they get so focused on the chase that they pay no attention to what else is around them.
These traits are why I would not use a sighthound to chase coyotes. First, they would pursue the coyotes . . .over hill, across fields, across ROADS . . .until the coyote is run down or escapes or the dog gets tired. If a more interesting prey should cross the trail, most sighthounds would drop the coyote and go after a deer or rabbit. In CT, a dog caught chasing a deer can be shot on sight . . . Also, the fact the dog would run across a road of any kind could easily result in a hound hit by a car.
The other reason I wouldn't use a sighthound to protect my chickens is a sight hound would love to chase fluffy, squawking, flapping chickens. Even though not all sighthounds will kill, a large fast moving dog can seriously injure or kill a bird unintentionally!