Build a 3 by 3 stone pillar taming pen that is 2 pillars high. Put one pillar (2 high) in the middle with and leave one side open (without one 2 High pillar) to kite the griffin in. Lead the griffin under the ceiling and into the pillars with a pteranadon (which can fly through pillars) and place pillars behind him to trap.
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.