I've been running dogs for several years now. They go with me whenever I am out hunting. They are fantastic on young, inexperienced coyotes. and also work well on yotes in areas where they have been called a lot and are very wary.
The idea behind using a decoy dog is to trigger a territorial response in the coyote. They create/trigger a need in the coyote to run the dogs out of their area. Their presence is usually enough to do the trick, but even more so if the dog(s) are aggressive in challenging the vote(s). Add food (a distress call) or young yote pups to the equation (early to mid spring for denning) and you can get explosive results.
The key is to use the right size and temperment of dog. If the dog is too big or too aggressive, the coyote will not engage, but run away (self preservation). Use too small of a dog and the dog will have trouble defending itself (run too slow to get away) or if it should it run into a pack.
I have come to the conclusion that dogs in the cur family are best suited for working with coyotes. The breeds include the Catahoula, Mountain Cur, Black Mouth Cur, Texas Blue Lacy, etc. All these breeds tend to fall between 18" to 21" at the shoulder when mature. Just about the same height as a coyote. The weight will be 40 to 60 lbs - a little more than a coyote, but not enough to make a yote think twice before engaging. These breeds have a great temperment with a lot of grit and bottom to face down or engage several yotes at the same time.
A shock collar with good range is an absolute must. The collars I use have a beep or tone button on them. That button is used for only one command: "Come Back! Come Back Right Now." This is how you get the dog to disengage and come back to you. The cotyote is led to believe the dog has had enough and is leaving. If the coyote does not follow your dog back far enough to come within range of your muzzle, you simply send the dog back out again. He re-engages the yote and then called off again. The yote begins to think that this dog just isn't getting the message and needs to be chased even further out of the area. Usually one to three engagements is all that is needed to get a shot at the yote.
The ability to shock is sometimes necessary in order to break the dog out of his tunnel vision. While neither dog nor coyote want to fight, both recognize that the encounter could quickly escalate to a life or death struggle. They focus all their attention to the encounter at hand and usually become oblivious to their surroundings. The shock helps to break the dog out of his tunnel vision so that he can hear the 'beep' commend to disengage and 'Come Back' - usually with the coyote it tow behind them.
I have had hunts where the yote was so focused on my dog that he sprayed gravel on my boots while coming to stop once he realized something wasn't quite right with his surroundings. At this point, I would never hunt yotes without my dogs. Too much fun and I love the companionship.