.22WMR is a different animal than the 22lr, but it's still not a proper coyote hunting rifle.
The .22WMR buys ~30-50yrds of extra range over the 22lr, but it's still not a great option.
The biggest reason you hear about so many of us using rimfires for coyotes is NOT because we bought rimfire rifles with the intention of calling coyotes with them. It just turns out that a lot of us have bunny guns, and decide to try them out for coyotes from time to time. Anyone that buys a rimfire with the intention of calling coyotes with it is either misinformed or mislead.
The "second biggest" reason you hear about it is that a lot of guys live in "Rimfire Only" zones, where they can't use centerfire rifles at all.
Then of course, there's the source of the misinformation, quite often being the ammo manufacturers. Hard to sell a rimfire rifle, or the ammo to feed it, if it's limited to a narrow band of bunnies and squirrels. But if they advertise that it's a great round for coyotes, especially in this hyped up predator hunting fad we're in now, it sells.
It doesn't make sense to me for someone to go BUY a rimfire rifle and intentionally limit themselves unless their regulations require it. A 22lr is only good to 50yrds, a 22WMR or .17HMR are only good to 100ish yards. Frankly, the new .17WSM is impressive, but a 20grn pill doesn't thrill me at 200yrds, no matter how fast it left the muzzle. A .223rem, on the other hand, will kill coyotes at ranges further than any hunter should be taking shots. I have a few 500-700yrd coyote kills with a .223rem, but I had to intentionally plan my sets to give me shots that long, and of course, had to have the right bullet to do the job and the shooting skill to give it a ride to work. I'd venture that there's never been a time that I really needed to shoot over 250yrds for coyotes. If I did, then it was my fault for planning my set poorly.
The long and short of it is this: In a pinch, if I have a nail to drive and a wrench at hand, I can drive a nail with a wrench. But that doesn't make it a hammer.
If I have a nail to drive and NOTHING at hand, it doesn't make sense to go buy a wrench to drive that nail. I should just buy the proper tool for the job at hand; the hammer.
So if you have a rimfire and want to try something new, limit yourself accordingly, and have fun. If you're buying a rifle, or are going to get serious about hunting coyotes, get the proper rifle. Get a centerfire.