So, to answer this question, I'll pose a question:

You're obviously considering the Handi-Rifles because they are cheap (why else would anyone buy one?), but I'd like to ask, are you wanting a cheap rifle because:

A) You intend to only hunt coyotes casually a few times a year or maybe not at all, so you don't really NEED a coyote rifle, but can justify a small expense on one?

or

B) You want to get into hunting coyotes more and have a limited budget right now and would plan to upgrade later?

Personally, if A applies to you, then the Handi-rifle will suit you fine. You don't need a $2000 rig sitting in the closet collecting dust just to go shoot a few coyotes every winter.

HOWEVER, if B applies to you, then PASS on the Handi-Rifle. Here's what will happen if you are actually going to get into hunting coyotes, which is to say, you'll actually go call coyotes more than about 2-3 times per year, on more than one or two years...

Someone that's just starting out, but plans to upgrade later will spend $250 on a handi-rifle today will use it for a year or two, all the while wishing they had something else, then either lose interest in calling coyotes because they're frustrated with their weapon, or break down and buy the rifle they SHOULD have bought to begin with. But, at that point, you'll be the proud owner of a handi-rifle, that really isn't worth jack (used prices around here are $100ish). Personally, I'd forego the wasted time and get a suitable rig. No, you don't need a $2000 rig to hunt coyotes ($700-1200 each on rifle and scope, give or take, for a top of the line coyote rig), but for $400-500, a Savage Package rifle (axis package, 11 package, etc etc) would suit you quite well.

For what it's worth, the Savage Axis base price (no scope) is $299. Personally, if the Handi is $250, and an Axis is only $50 more, I know what I'd be spending my money on.

Even in that price range, a higher quality USED rifle would be a far better option. I bought a used Savage/Stevens 200 for $200 back in '09 or '10, and the guy threw the 3-9x40 bushnell scope in for free. I bought a used Savage 10 last year looking for a donor action for a custom build for $450.

The general question for coyote hunters is "do I really need an AR-15 for faster follow up shots?" Most hunters with bolt guns will, at one point in their hunting careeer or another, feel disadvantaged even carrying a bolt gun, since a semiauto would have faster follow up for doubles or running dogs. Ask yourself, how fast can I really be with a single shot break-over? Not likely that you'll even be as fast as a bolt gun, let alone a semiauto!

Sure, a Handi-rifle can work, and yes, you will be able to kill coyotes with it. But no, I wouldn't say I'd recommend one.