Ulu, is amazing for deer and fatty kind of animals and the best part is that once you get the hide off you can almost perfectly flesh it on a dead tree right where you are. THe best Ulu knives i have seen are stone, they never seem to get dull.
As for skinning a coyote.. Or Bobcat. I wouldn't use it. Those hides are very thin, and to be fair, you really don't use a knife a lot skinning a coyote or bobcat. Not where an ulu would be helpful. Unless you did some fleshing once you skinned it down to the front legs, and before removing the hide completely.
If you are using your knife to skin more than half the time you are skinning, you are doing it way way to much.
If anything, if you are skinning coyotes. You need a knife to cut the initial cuts, a thin one skinny 3-6" blade works really well for ringing the rear legs, cutting off the front legs at the first joint above the dew claw, and making the cuts from the ringed rear legs up the to bum, One side go over the top of the vent, and the other side go under the vent or female parts to connect with the first cut. Then i run the blade down the underside of the tail from the cut line usualy 3" is good. (just to get that started)
Skin around the ringed legs a little to get it started, then put the knife down and pull.
You will need the knife at when you get close to the tail. Then a tail stripper is a good little tool you will be glad to have.
Then i pull and pull, until the arm pits. I have a long flat tip screw driver that has a just undersized 1/4" hold drilled in the handle for when it snows and i need to put the decoy up higher. I can stap that in the ground, then put the decoy into the handle. The rest of the time i use it to get between the armpit and pull off the fur from the front leg. (both sides)
I don't need the knife until the ears, eyes, and mouth.
I know there are speed demons out there, but after practice If you use the right techniques it takes me about 10-12 minutes to skin a coyote without rushing. I also have a small radio to listen to while doing it.
Here is my skinning rack, the guy skinning is from Scottland and i took him out for a few days, and he is skinning one that he got.
I found that a 10' piece of 1 3/4" .120 wall square tubing was perfect. I cut it and welded it to make this shape and then put a sleaved it to make it so that i can take it apart. I also use it to wench an elk into the truck with in the fall. (hence the reason for the .120 wall) It's plenty stong for the pulling and tugging.. I plan to change it slightly with either a boat wench and roller guides or something to make it so that i can start low, and then raise it as i get closer to being done. I also think i will add the fur holds, so that i can use the wench to just pull the hides off. If you have ever tried to skin more than one or two at a time, you know that after the third, your hands start to get tired.
You can make a good fleshing beam from a log. I cut it into a rough beam with a chainsaw, then hit it with an angle grinder to put a slight bevel on the top and more on the sides. (use the meansurements from NAFA stretchers for your guide) for the bevel I used a 5 gallon bucket as the amount of curve you want on top.