Build a 1x1 out of thatch or whatever your heart desires, grab an argy and drop one in it. You can pet it through the wall! BOOM! Done. I used wood foundation and thatch walls that were lying around. Must be walls, so it can't "see" you. Mine had its head sticking through a wall and I got super close and just started petting it like George from of mice and men.
Normally you can't tame the pack leader, so just get a pteranodon or argy, pick it up and drop it in a large area (like a separate section of your base). When you take it away from the rest of the pack, it removes its 'pack leader' title, allowing you to tame the highest level hyena of that pack.