Breed rexes/spinos, hatch and pod the babies. The more - the better, you never know when things will go wrong.
Take a good shotgun, some ammo for it.
If you have a desmodus - gather blood, make a sanguine elixir. Also take some blood with you - you might get hurt.
Put on some good armor and take a sino.
Find the carchar, take a bit of ammo and a few of podded babies with you. Leave rest someplace safe but close enough (hard to do with a wild carcha nearby, but try).
Wait for carcha to kill everything near it and calm down. Unpod a baby, shoot it, drag it to the carchar. Hold it until the carchar sniffs it, then drop it and use your sino to get away. All three carchars I've tamed only needed one to get friendly, but highest of them was level 90, so i don't know if max level will also be friendly after just one. Better safe than sorry - after all, you CAN afford that bit of extra time, since you got your snackrifices right in your inventory and killing them doesn't take long. if dropping the corpse form a ledge - make sure carchar can reach it in 1-2 tries, otherwise it won't count when it finally eats it (I guess your scent will wear off).
No trap needed. With low levels you can use sanguine elixir (if you decide to use it) during first run, but as my experience with taming a level 90 shows, with higher levels it's best to save it for later, in case things go wrong and you have to go home for more baby dinos.