The method i used was to aggro him and use a Basilosaurus(big whale) and go to the surface where he will just keep reggening and while the plesiosaur is focused on my Basilosaurus i just get out my crossbow and pelt him with arrows
There is a glitch at the redwood on the center, where plesiosaurs will spawn really near the coast and whole groups of 2 or 3 are glitched in the water, meaning you can knock out multiple plesiosaurs at the time.
The trick is to argo one, have him chase you into an underwater cave where he will not be able to fit through the door but his long neck and head does. when you do this he will not de-agro, you can then get a clear shot from the cave with a bow and tranq arrows
After tamed, you can grapple onto them while a tribmate drives it and easily tame more large water mounts. If you are about to touch a structure or terrain, crouch to take off the hook or you will die instantly and your body will fly across the map
The trick to ko these guys is to wait for them to agro you, once they're close enough, swim up and backwards until you've reached their swim limit and shoot them as many times as possible. When they lose interest, just do the same trick and eventually you'll knock it out