Pick up with wyvern or argy and out in taming pen. That's your best option for taming. In official games I don't even think they're worth it as they require sooooo many narcotics! I definitely recommend 3 or 5 if you get them though
When taming, shoot from a distance so you can get 2 or 3 tranqs in them and then they’ll run from you. Chase after them while shooting and it makes taming so much easier. Have lots of narcotics ready though
I reccomend building a taming pen 6x2 with doorframes around it... And then go to tbe beaver spawns. Pick one up with you argentavis, (yes you can pick it up with an argent) and bring it back to your taming pen. Tranq it with arrows or longneck rifle and feed it some gallimimus kibble. Make sure you keep an eye on the torpor because it drains pretty fast. After that enjoy your perfectly tamed beaver.
So, I live in the footpaw and I've learned that to get these you either need to go through the titanoboa in the writhing swamps, or the spinos at the end of the beach. Choose one, I recommend the spinos because you can knock them out by standing at the top of the cliff above the beach and shooting them full of tranq arrows.
To help more than the calculator can, bring along 300 Narcotic, 200 mejoberries and 100 other berries. This is the rough average for these things, up to like level 180 or something. Hope my tip helps with taming! And make sure to build a 1x1x1 base made of stone, if you want to target one to tame!