Alright, let's look at lagomorphs. The European rabbit is the source for domestic rabbits and there's a ton of domestic rabbit breeds. However, it's stated that the Cliff Dwellers or Ancestral Puebloans might've practiced cuniculture and European rabbits would not be the source for that. So let's look at some alternates...................................
Pygmy rabbit=Smallest leporid, but able to breed at a year. Doubtful due to their size, unless they could be bred up.
Volcano rabbit=Second smallest leporid, specialized diet, but can breed in captivity.
Riverine rabbit= only has one offspring, yet are beneficial to farmers.
Hispid hare=Not much known.
Striped rabbit=same
Bunyoro rabbit= nocturnal, stable, hunted by locals. Unsure.
Red rock hare=small litters, can breed at a year old and year round.
Cottontails= Varied, since there are at least 20 species. Although some, like the marsh rabbit, swamp rabbit and desert cottontail show greater potential than others. Bonus for the disease fanboys here in that they're carriers of myxomatosis, Or at least show greater resistance than their European kin. Also have sizable litters and mature fast.
European hares= Among the largest of the leporids, is hunted and eaten throughout Europe and breeds very easily. Also a little violent and among the fastest mammals around.
Antelope jackrabbit=Large, tough, can breed easily, was hunted for food and pelt. Possibility?
Snowshoe hare=Nocturnal, cannibalistic?. Well, it might be a decent micro-livestock in northern climes.
Arctic hares= Don't fare well in captivity. Unknown about the mountain hare or tundra hare.
Basically, hares are larger than rabbits though faster and has less meat on them. All of them were at one time or another hunted for meat and pelts. Another use for domestication might be wool. There are breeds of domestic rabbits used for that purpose, so more leporids domesticated for fibers would be interesting.