Maybe. Depends on how different wolf piss smells compared to dog piss. Also, an unaltered male wolf is going to have different smelling piss than a neutered male dog, and that might make a difference. Probably the same for females, too.
We don’t get too many coyotes where we live. But do keep our cat inside for fear of foxes.
This is really a side note and I hope that the OP finds a solution. I think human smells may be the way to go. However, the one way I have found to keep black bears from ripping off the door to our shed is to crush moth balls on the steps and near the door. One snoot full of that I’m sure is unpleasant.
Perhaps scatter some moth balls around the property?
I have never used predator urine to keep rabbits and other pests out of my yard, because of the manner of its collection (through floor drains in animal cages).
Marketed by one company as “the all natural, organic and humane way” to defend garden borders from wild nibblers, bottled urine is anything but humane. The product comes from fur farms, says Mary Beth Sweetland, senior director of investigations and research at The Humane Society of the United States. Produced also for hunters as a way to hide human scent, the urine is collected from coyotes, foxes and other animals raised in wire cages. Earlier in her career, Sweetland was part of a 1990s investigation that captured sickening images of the animals’ pitiful lives, including a particularly haunting one of a fox with his right front leg bone exposed. To feed the animals, the company ground up live hens in wood chippers. “Nothing has changed insofar as how urine is collected,” says Sweetland. “It’s all from caged animals on fur farms.”
Er… really?
Since when is coyote fur a thing?
Also, the product I have used for several years claims to have come from a zoo, not a fur farm. Admittedly zoos aren’t necessarily a paradise for the animals, but these days they’re hardly hellholes.
And WTF with the “hens in the woodchipper” thing? Do you realize what kind of mush that would result in? Why bother when you can just kill the hens and toss them in the cage for the predator to take apart itself? That just doesn’t make any sense. I think it far more likely fur farms would be using “Purina fox chow” or whatever, nice, pre-made pellets that are nutritionally balanced and won’t go off nearly as quickly and hen mush.
Need more cites than one obviously biased website.
There are a few artificial/chemical versions out there for someone really afraid of fur-farm channels.
But — fur farming is so heavily regulated and inspected that abuses are a small percentage of the equation. If you are seriously vegan or opposed to the farming of any animals, look to synthetics. But other than that you can use with some level of confidence.
https://www.predatorpeestore.com/How-Do-We-Collect-The-Pee-.html
To be honest, I have trapped in the past and may again some day in the future so I’m not without bias.
Just a word of caution … whether predator pee repels garden pests or not … it will attrach predators … that’s why it’s commercially available to the trapping community … splash some cougar pee on a tree trunk, put the trap right underneath, when the local cougar comes along and smells the pee it will try to overmark it with their own pee … then snap … you’ve a fine pelt.
If Deanna wants to mark her own territory 
, I don’t see any harm in it. The worst thing that would happen is that it won’t work.
Predator Pee also keeps away Schwarzeneggers.
…They’ll be back…
And bring Aliens with them.
The OP better find out if it’s illegal to pee in their yard. If people use wells for their drinking water this could be a health hazard .
Thanks so much for all the replies!
I’m still a little skeptical about the predator pee thing, but I am going to look into the logistics of using some of my own personal stock . I promise I won’t actually go pee in my yard…but maybe I can collect a sample and leave it along the edge of my yard where the woods begin.
I’m also still thinking that there must be a way to get them removed, before the population increases. I really think we’re dealing with just a few animals at this point, not a full-blown invasion. I have brought it up to a member of Town Council, and I think I may pursue addressing a Council meeting, to see if they can offer up a solution, or any type of assistance.
In the meantime, I can enjoy the nightly serenades, and keep a close eye on my now mostly indoor doggies.
My neighborhood is surrounded by protected wetlands which includes a park, and, on one side, a golf course. Hearing coyote howls in mid-spring through summer (the pups are born in Feb-March) is a rite of passage around here. I occasionally see “the old guy” on my way to work (I call him this because he’s obviously the pack leader given his size) . He doesn’t like humans so he dashes into a backyard if he sees me.
Almost everybody in my neighborhood has a fenced backyard and never leaves their small dogs unattended. Cats are indoor cats.
We have stringent wildlife laws around here. Coyotes can only be hunted one month out of the year and cannot be hunted within X yards of a main road, which basically excludes my general area. I suppose if this was a rural area and people had livestock, it’d be another matter, but it’s not, so…
Live and let live. They won’t bother you if you bother them. I find them fascinating 
I suppose you could term the Humane Society “biased”.
*"Allegedly collected from coyotes, foxes, bobcats and other animals, predator urines may be variously billed as safe, organic and humane. Safe and organic these products may be, but humane they are likely not. Predators aren’t known to urinate on demand at collection stations in the wild. Judging by the volumes that increasingly line the shelves of garden supply stores, logical sources of predator urine are the thousands of wild animals raised on fur farms.
Animals at these “farms” – often little more that a series of small wire cages in an open shed – are bred and raised for their pelts. They suffer from extreme confinement, poor housing conditions and die inhumane deaths.
Far more effective and humane alternatives for resolving wildlife conflicts abound, including fencing, netting and repellents."*
And:
“Don’t use repellants that contain the urine of predators, such as bobcats or foxes. This urine is often collected from animals that are housed and treated inhumanely.”
For the OP, it’s hard to imagine what sort of predator urine would keep coyotes away. Coyote urine could well act as a mating call, and human urine is said to be so low in pheromones that it doesn’t even repel deer (which also didn’t care about coyote urine in one relatively controlled study).
In the '90s, I worked with my friends at the local Renaissance Faire; my friend owned a blacksmith shop there. One summer, a family of skunks moved in underneath the shop. Someone who claimed to be knowledgeable about such things advised us that “marking” the shop with human urine would, indeed, encourage the skunks to seek new lodgings.
So, that Saturday evening (the Faire ran on Saturdays and Sundays, and we’d spend our Saturday nights at the shop, drinking beer and grilling), all of the gentlemen were encouraged to relieve themselves against the outside foundation of the shop building, rather than heading to the usual port-a-potty. It did, in fact, work; the skunks were gone soon after.