There're a couple of counties in the Valley along the border that have a reputation (and the records) for MONSTER whitetails. FWIW, I shot a buck in Uvalde Co that went 200 lb on the hoof. [That said, we're pretty sure that he had been one of the imports from up north that a local rancher had tried to stock on his place, only to lose it to a washed-out fence. His loss-- my gain.
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There're more ways to go than it bears gettin' into. There are the nifty pumps and autos from Remington and Browning in real calibers (I once had a distinct yearning for a Browning BLR lightweight in .308, which would allow the use of spitzers.). There are the venerable lever guns from Winchester, Marlin, Rossi, and Puma. (I've still got a yearning for one of those .454 M'92s). There is of course the above-mentioned, much-loved Savage M99, with which a man could kill any deer that ever walked in .250 Savage. The .300 Savage caliber gives a bit more thump, but isn't quite as flat.
You didn't mention why a bolt was no good for you. If it's the speed of second shot, then you won't be much interested in the single-shots out there. But if you would consider them, highly-accurate and economical offerings are available from NEF and Thompson/Center, and quality single-shots are available from Ruger.
There are those who like to have their military type guns do double duty. I know people who have taken deer with an AR-10 (both with .308 and .243 uppers), AR-15, and SKS rifles. I have seen my father take his M1A Super Match Grade into the field in search of deer. (I'm giving real thought to taking that same rifle to a turkey shoot match tomorrow, actually, for the 50-yard Standing with open sights round.)
The choices are legion. (And that's a
good thing.)