There are coyotes in every state of the Union, except Hawaii, and in Virginia the state actually pays folks a bounty to kill them. This story about coyote hunting with greyhounds in Oklahoma appeared in The New York Times in 2010, with audio and picture goodness at the link:
Hunting coyotes with greyhounds goes back generations. President Theodore Roosevelt did so on this land, about 70 miles southwest of Oklahoma City, in the early 1900s. It remains largely a regional pursuit that is part of the area’s lore, like the cattle drives along the Chisholm Trail..
...Rancher John Hardzog... has 40 greyhounds and greyhound mixes, some with scarred legs and faces, that he bred on his 318-acre ranch. Sometimes, they gnaw on stillborn calves and clean their teeth on the bones. He said he spent $600 on their monthly upkeep.
They have names like Matthew, Luke, Venus and Little Bit. Some are part Irish wolfhound, others part Saluki. All have a strong prey drive and hunt by sight. Only a handful have failed as coyote hunters, Hardzog said.
Electric-shock collars help train the dogs not to chase anything but coyotes. Otherwise, Hardzog’s dogs are collar free, for good reason. Several broke their necks when their collars snagged while scooting under barbed-wire fences, which can also rip their paper-thin skin.
“Every time you turn ’em loose, you don’t know whether it’s going to come back sound or not,” Hardzog said. “There’s just a lot of obstacles out there. Every once in a while, you had one run off in a ditch and either break their back or a shoulder or dislocate a hip. But it’s the risk you take. If you didn’t let them run, you would be denying what they were bred to do.”
Once, Hardzog lost four dogs when they ran over a cliff while pursuing a coyote, his wife, Charlette, said.
“He has such a bond with his dogs,” she said. “He could barely get over that.”
In his truck, Hardzog often keeps a blood-clotting agent, wound wrap, a staple gun and an array of medications, but no water. If a dog is seriously injured, he said, he takes it to a veterinarian. Other hunters might not be as caring, he said, because “they got no common sense.”
...Hardzog hunts from Thanksgiving through March, killing 270 to 350 coyotes a season.