If you have an argentavis, grab the procoptodon on the claw of the bird and let a friend fire him some tranq arrow / dart. If you don't have an argentavis or a quetzal, then, trap him with bolas and fire him. Bring some wood / stone fence foundation and some wall to build around him to be sure that he's not attacked by any wild creature and be sure to have a lot narco / rare mushrooms. When tamed, a procoptodon is fast and he's a great Dino to tame other since you can jump in his front pocket and fire weapons. Also great in scorched earth when you're trapped in a sandstorm.
Get rare mushrooms from the swamp, not the the tall trees but the ones that have multiple roots going into the ground. Use a metal pick axe too! You'll know the difference between trees when you see them
Can't be carried by an Argy, have tried this multiple times. There's a strip of land at the top left of the Island which has snow and beach. Head up and down the strip and kill any Predator until the procoptodon spawns.
These things are very easy to knock out. Just bola it and then use tranq darts to knock it out, tranq arrows work too. WARNING! They eat Rare mushrooms and/or Plant Species X seeds so gather up a bunch and you'll be set.