Personally, the .17HMR and .22WMR are "moderate range" rifles for coyotes, not "longer opportunity" rifles.

Like Sheridan said, that 12ga will suit you fine for these dense brush shots.

If you want longer shots, step up to a centerfire 22cal, like a .204 Ruger, .223rem, .22-250, etc etc etc.

I have taken a lot of coyotes and bobcats over the years with a .17HMR and a .22WMR, but I only use them because I own them. I wouldn't necessarily recommend you go out and spend hard earned money on one as your dedicated coyote rifle.

If all you can afford is a rimfire rifle, that's a different story. In my experience, both kill coyotes dead at 100yrds, and neither has necessarily a huge advantage over the other. The .17HMR is flatter shooting, so some people think that makes it more accurate. Personally, I don't really see any practical difference for 100yrd coyote hunting.

Ultimately, if you're going to spend $400-500 to buy a rifle to extend your coyote hunts from 40yrds to 100yrds (buying a rimfire mag rifle), why not just spend $500-700 and extend your hunts to 600yrds (buying a centerfire 22cal)? The impact of your investment will be MUCH greater if you step up to a centerfire 22cal, or even a 6mm or quarter bore (.243win, .25-06, .257Roberts, 6mm PPC, etc).

My recommendation would be to get a .223 or .22-250 in a Savage bolt action, drop on a 3-9x50 or 4-16x50mm scope, and knock yourself out.