Just about any docile grazing animal will do.
Everything we have domesticated at this point was indigenous before we started domesticating it, so that constraint of "needs to survive in the wild" doesn't make a whole lot of sense. If you mean something that could survive if its farmer died... Maybe someone could help narrow my list down.
Yaks and Water Buffalo
Both were raised in antiquity and mirror cows pretty closely in functionality.
Thanks to John for this one
Sheep have been used as a food source in many cultures historically. As a nice bonus, you also get wool
Llamas and Alpacas
Llamas are the feistier of the two and both were used more for their "wool" and packing ability, but they could conceivably be used as food sources.
Horses, Donkeys, and Oxen
There's no biological law preventing the consumption of horses, donkeys, and oxen. It's just we found they were more useful as beasts of burden because of their strength and stamina.
Exotic, But should work just fine. Probably better for packing through desert climates, but is certainly a viable food source.
These haven't been used historically, but are chill enough to domesticate for meat. The major issue is that their reproductive rate is quite low- about one offspring per two years. Secondary to that is that tapirs are nocturnal and compete for the same food sources as humans. They're more likely to simply be hunted than domesticated, though pet tapirs are not unheard of.
Some non-grazing animals could work as well
Rabbits have been eaten and farmed by many societies throughout history and can even be found in supermarkets today.
They're a little tricky since they're smaller, have more predators, and burrow, but are a viable food source because of their high reproductive rates. Since they're so small, you can have rabbit meat fresh and don't really have to worry about preservation.
Thanks to jamesqf for making a case for including rabbits
Guinea Pigs and Capybara
Basically the same deal as with rabbits, but indigeneous to South America.
Goats and Pigs
Goats and pigs don't actually graze; they browse. This effectively means you have to actively feed them. I suppose you could also use forest land as well, but that has its own set of problems.
The nice thing about goats is that they eat just about everything, so leftovers and scraps can go to the goats. You also get milk, so they can more functionally mirror cows.
Pigs are not as efficient as you might think and pork is hard to preserve without refrigeration. They're also quite a bit pickier than goats, so you may end up with more waste from their slop feed.
Chicken, Turkeys, Ducks, and Geese
You have to do something about their flying, so you either need to have a lot of land, put them in cages, or clip their wings. Turkeys are the least problematic of the four.
You also get eggs. That's a nice bonus.
Thanks to jamesqf for making a case for including fowl
Since snakes are ectothermic (cold-blooded), their being carnivorous isn't as much of a problem because you don't have to feed them nearly as often. They have pretty large litters as well. I'm unsure about growth logistics and meat efficiency.
The biggest problem is that containment is very difficult (much harder than with rabbits). Fences aren't going to work and walls might still fail to contain them.
Thanks to John for the point on containing snakes