There are all sorts of dog reactions to a coyote. Some dogs never see a coyote which is right there in the open, some stop and look, some go after the smell without even seeing the coyote, some chase, some bark and chase, and some dogs ignore it.
Dogs seem to be calmer and more in control when they are leashed. If a dog is on a leash, obviously it will be the owner who is calling the shots, whether it is a mild dog or an active one. An owner can easily drag his pet away from a coyote if it is leashed, rather than having to call a distraught dog to him/herself first. Yesterday, someone told me of a bizarre incident which happened a year ago: that they were jogging early in the morning with their dog, when a coyote came in at them from the side, making a running leap to land on the dog. This itself is very unusual coyote behavior and the only instance that I’ve heard of it. The dog owner was able to yank the leashed dog, and the coyote missed its target! This happened last April, which is the prime pupping season — coyotes are much more territorial and protective of their areas during this time.
If a dog is not leashed, there are several ways the dog may react to a coyote. If the dog is more timid and obedient, it may look to the owner for what to do: the dog will either stay beside the owner or come when called. Some dogs have been told in the past to stay off of the coyote, and they do so. One of my friends has an obedient dog, which has been told to stay off of the coyotes, and it always does so. On one occasion, this dog hugged its owner’s leg as it walked. The owner sensed that there might have been a coyote around, even though he never saw it — the owner told me this was very unusual behavior for this dog. In this case, the dog was trying to communicate unease to the owner.
The majority of dogs are somewhat curious about coyotes — they know the coyote is something “different” from other dogs. But different dogs have different degrees of apprehension or fearlessness or sense of fun and adventure regarding the coyote, and they act accordingly.
If a dog is not leashed, and the dog is an active type out for its free run, the dog will often chase the coyote, thinking this is great fun. It may end up barking incessantly at the coyote once it gets within about 15 feet if the coyote does not flee. The coyote will easily outdo the dog in length and intensity of barking — this becomes boring or tires out the dog. However, it is only when the coyote turns to chase or nip at the dog that the dog really starts to think.
Please see my entry on “Coyote Safety” of 11/3, as well as the three entries on how coyotes react to dogs: “ANOTHER reaction to dogs” on 11/17, and “Some reactions to dogs” on 11/04. “Significance of a Seemingly Unprovoked Challenge” on 12/1. “Blatant Visual Message for Newcomer Dog” on 2/8/10. “A short back-and-forth chase:oneupmanship verging on play” of 2/4/10.
Coyote Yipps 
Sep 01, 2017 @ 12:59:05
Our 20lb dog visited with us and stayed with my parents when we traveled so he knew their property well for leashed walks. One trip he was acting strangely and refused to go out in the usual walk direction for days. We later realized he was keeping himself/them/us away from a coyote pack that was feeding on a deer carcass under one of the pines on their property. Thankful that he wanted nothing to do with them.
Sep 01, 2017 @ 15:37:54
Hi Tricia — Thanks for your comment. Although coyotes don’t approach people, your little dog is vulnerable. Some dogs, as yours, are very savvy enough to keep away from them, but not all dogs are. Here is another fairly small dog who knew it was best simply to leave the area: Coyote Encounter During Pupping Season. You have a smart little dog! :)) Janet
Dec 25, 2017 @ 14:13:00
On Christmas morning, I let two Yorkies out unleashed to pee. I noticed unusual behavior in the darkness. One dog was sniffing an area he doesn’t normally sniff and the other one was in a stance. His eyes was locked on an object. I looked and saw a big object staring at him in the middle of the street. That is when I realized it was a coyote. I yelled for the dogs to come and yelled and clapped my hands. The coyote ran towards but then retreated.
Dec 25, 2017 @ 19:09:00
Hi Alexandria — Dogs often are more aware of their surroundings than we are — and your dogs appear to have been. Your dogs’ behavior clued you into the fact that something unusual was going on out there. You now know that coyotes are in your area, so especially when it’s still dark, always keep your small dogs leashed when you take them out. Then, if and when you see a coyote, simply shorten your leash and walk away from it. If the coyote keeps coming too close to your dogs, pick up a small stone and toss it towards the coyote (not AT the coyote) angrily as you keep walking away. Here is additional information with which to prepare yourself: How To Handle A Coyote Encounter: A Primer, and How To Shoo Off A Coyote. Have a safe and happy Christmas with your pups! Janet