I play on singleplayer, make sure the one you wanna tame is alone and doesn't have it's buddies arouns, bola it and knock it out usinf tranq arrows, took around 100 mejorberries and 20 narcotics. Time? Around 20-30 minutes.
If you want to get a lot of pelt, make your base by the hidden lake on the Island, you can look up coords. Beavers spawn there, then harvest their bodies with pick. Don't worry about overhunting they just spawn again. And free dams.