I've developed a method for taking out these beasties whilst you (and, hopefully, the carno) are still in the lower levels. Grab yourself a bow and a few handfuls of tranq arrows, and then play a game of 'catch me if you can' with your foe. (Hopping up on rocks, running in a zig-zag pattern, and taking advantage of tree trunks works well for me.) As you're running and dodging, lob as many arrows as you can into the beastie's snout. Fair warning: you're going to get bit. But a dozen or so arrows later, the tables will turn, and the Carno will attempt to make a run for it. At this point, just trail behind and wait for them to drop. Voila! Either dispatch or domesticate the fallen fiend. I don't know how many I've ended in this fashion, but enough to have faith in the functionality. The highest level Carno that I've taken out with this sprint-and-shoot method was only about a 30, however. Of course, this'll become redundant once you become powerful enough to take one head-on.
Carnos have a “blind spot” where they have trouble hitting you. If you get under their chest, then they have trouble attacking. Sometimes they’ll put you in their blind spot on their own and just stop attacking. I’m on mobile btw, so idk if it’s the same on console/PC
So back when i was a new ark player i tamed 8 raptors just for defense, later on i spotted an alpha carno walking down the beach towards my base, and not wanting my newly tamed sarco, and trike to die, I did something any normal person with 8 raptors would do. Me and the pack and charged into battle, lets just say i lost all but one, Silver. Shes still alive today and happy, And we did kill the alpha carno.