An easy way to keep a carno at a good enough range to hit it safely with tranquilizers is to build a wall three wide and three tall on fence foundations with two doorways stacked on top of eachother with no doors to shoot through. Then, aggro the carno and lead it to the wall. Then run through the door way to get it stuck and proceed to KO it.
I recommend, if u don’t have a spyglass, to get enough arrows for a 150. Just in case the Carno you have your eye on happens to be that. I tamed a lvl 60 but outrunning it with my raptor and shooting it with arrows. Its not easy, but it gets the job done without having to build traps and stuff like that. You can just bear trap it and knock it that way.