I like the clean lines of the classic pump rifle, the Browning designed pump mfg by taurus, so far has been the best performing gun right out the box. my left hand never leaves the wrist and follow up shots are amazeing esp with the .22mag rimfire.
FOR Right handed shooters one may try the Ruger Model 96/22mag, another wonderfull box mag rimfire magnum.
I'd say try a .22Hornet barrel on the Handi Rifle, You'd be amazed, its like a .22mag on steroids! the range is ok, the authority is a whole step up in performance and the rounds wont land in the neighbors cow pasture a quarter mile away, and when you discharge it half the township wont roll out their recliner to see whats up.
Then again a 218 bee or a .32-20 would be my fave coyote lever blasterat limited ranges.
mabe a Marlin model 62 levermatic in .30 carbine or .256 winchester magnum (necked down .357magnum)
Hello REX!
I can say I BEEN THERE DONE THAT

and your spot on with your comments!! (Sans the Taurus recomendations, too problem attic for my taste

)
I had a Marlin 62 in 256 Mag about 15 years back, I still have a beautiful old Winchester 43, chambered in 22 Hornet.My Pop has its twin in a 218 Bee. I also have a Handi in 22 Hornet. Your correct its a great shooter!!
I also had and sold off a Ruger 77 in hornet (44, 22H, 22LR & 50 cal) cause it would not shoot well enough for me. (That's the same for the entire line!! 22LR/22M/22Horn/44M and 50 muzzle loaders) I also had a 96/44M (Never the 22 or 22M versions)for a short while, but the Marlin was SO MUCH nicer I sold the Ruger and kept the Marlin '94's
I still have Marlin 1894CL's in 32-20 and 25-20, (In a moment of stupidity sold off the CL in 218 BEE) a Savage 23b in 25-2 and a H&R stubbed barrel in 32-20, GREAT little rounds!!

I use the Savage 23 quite a bit for coyotes too, its long barrel makes it a natural for peeps and I love shooting it! I have a nice 60G pill shooting along at near 2000 fps. It aughta turn lungs to jelly!
I WISH Remington had come out with a 22M version of there little BDL 22LR pump guns!! I have also shot a Browning pump 22Mag a friend had it was a nice gun too. Marlin had a 22M auto for a while too. I would buy anyone of them on sight!
The "next"

22Mag will likely be a Henry Golden! (After my PMR comes in of coarse)
CW