whatever else 'yotes are, brave they ain't
9mm might not be best choice for 'yotes unless you are well practiced with one (and your lady is also)
12 gauge might not be best if your "best friend" gets a little too close
both are more than needed at short range
coyote hunting is a different thing, but making them go way does not require all that, especially at range anything like named
they are not going to charge you or your dog if fired upon
22 mag is loud, but not that loud, and will kill 'em (handgun or longer), not just make 'em run way when hit
any 22 rimfire will make 'em leave fast, might (likely will) come back if not hit, will not come back if hit... though not brave, they ain't stupid, won't hang around, lacking 'motivation'... (they are scavengers)
a cheap single action 22 revolver will do
any 22 rifle will do better, unless well practiced with a 22 handgun
cheapest 22 rimfire you can find will do
if not real good on running shots, don't bother, you won't get one anyway
fair argument for shooting once, not dumping a mag
hit or miss, one shot will suffice, mind your backdrop and dog if inclined to shoot more than once
if not a practiced rifle shot, a cheapo red dot on any cheapo 22 rifle makes it pretty hard to miss a yote at 30 yards or less
hit or miss the same yote will never give you the Terminator "I'll be back" look after 1st shot fired
and any cheapo 410 single shot hammer shotgun with a slug will drop 'em as dead as it gets at such modest ranges, pretty much any body hit... fancy not req'd.. and real safe until you pull the hammer back..
PS
or get a german shepherd ("working dog" flavor, 90# or plus, not "show dog" flavor) 'yotes are neither brave, nor stupid
german shepherd dawgs are both brave and smart, and were bred to fight wolves
(wolves are smart, too, smart enough not to take on a big GSD one-on-one, but smart enough to bring friends, you got wolves, bring friends and a bigger gun than a 22, 'cause a "family" GSD will not back off, but can't handle a pack by themselves... want a friend, be a friend)