Make a 3x5 taming pen 3 walls high dino gates on either end and a door. Use Pter to aggro and Griff will chase you inside. Wait till it shut dino door and open and fly through reg door with Pter. Shoot with TOX arrows from open doorway. Balm, griffin kibble and use 1 bio everytime torpor drops down 80 from full. GOOD LUCK
Just build a 2x4 or 2x6 pen with a dino gate on one side, placing stone pillars on the outer edges all along it. Make it near the green obelisk! Then fly the griffin into it thru the door with a pteranodon, fly out thru other end thru the pillars, land your mount, run to the other side, close the door, boom. Trapped griffin. Then tame with roughly 150 tranq arrows. Use mutton or prime meat as they are easiest to come by.