Forget semi auto, maybe try the Troy PAR. At least it seems like a quality rifle that looks cool.
Any non restricted semi you find for under $1000 is going to be a POS. If you can wait the WK180-C should be coming sometime in the next few months but it will eat all your budget before glass.
The best hunting rifle in my opinion is a bolt action. You don't need fast follow up shots if you actually hit what you're looking at and if there's more than one you should be able to get at least a couple before they skidaddle and are out of range.
A quality semi auto is going to cost $1500+ used.
If you can get more cash together I'd look at
HK SL8 series, I've owned 3 of them over the years and they are the most accurate rifle available out of the box. HK quality, HK reliable, and the Lothar Walther barrel is the best factory barrel available. Only downer is ergos aren't for everyone and mags are expensive.
XCR-L (newer the better), not the most accurate but good enough for coyotes, great warranty, under $2000 used, AR magazines.
ACR if you can find a used one for the right price, I own an ACR and it's accurate, reliable and probably the best option we currently have for non restricted (after conversion).
Tavor/X-95, again not the most accurate but reliable and compact. Used to own one, wasn't for me.
Skip the mini-14, I've heard the newer ones are better but the one I had was horrible for accuracy and I wouldn't shoot at an animal with one if they're anything like the one I had.
SU-16, I've shot 3 of them, the two folding ones grouped like a shotgun but the tactical version with the AR furniture wasn't bad at all and felt better built than the regular version but a pain in the ass to clean.
T97, made in China, no warranty, no parts support, not worth $500 in my opinion.
Used AR180B-2, about $1500-$1800 used (discontinued but RWA is making parts for them), light, accurate enough for yotes, and a really neat rifle that you don't see too often. I love mine and will never be selling it.
You could switch to 7.62x39 and try a type-81, another crappy Chinese built rifle (I own one) but it's reliable, $1000 and doesn't need optics. Mine shoots about 4 moa with the irons and my old eyes that prefer a diopter style iron sight.
Skip the x39 M-14 though, lot's of reports of broken bolts. The new ones are cast and seem to be failing regularly.
There are more but those are the main ones that come to mind right now.