Been there, done that. The 1885 is a great rifle, in terms of accuracy, style and strength. If you're looking for a handier rifle, I'd suggest looking for a "low wall" in .223. It's considerably lighter than the high wall (which is what your 22-250 is likely to be found in). One of my classier gopher rifles is an 1885 low wall in .221 Fireball (rechambered from .22 Hornet).
It absolutely delivers devastation on the little varmints. The 1885 low wall can also be (occasionally) found in .243 Win

which makes a formidable 'yote round.
Practically, though, if you're going to be hunting coyotes, you'll be doing it in cold weather. Bear in mind that the Browning has an exposed hammer, while the Ruger has a tang-mounted (sliding) shotgun-type safety. With a scope, there's simply not a lot of room for a gloved hand to "thumb" the hammer back (or down) on the 1885.
Sure, the No.1 requires a scope with a lot of eye relief (Leupold, Burris or Zeiss will do the trick), at least, when the time comes that you want to apply (or take off) the safety, the No. 1 will do it with more certainty, in my experience.
FWIW, the 1885 high wall makes a significantly longer and heavier package, whatever caliber it comes in. (Great for a big game rifle, though).