Make 3 stone dino gate door frames and then 2 gates and then place them in a row close but not to close to where the griffin can fly out and then place 1 gate on either sides of the trap and then trap the griffin inside and you can easily knock it out from there.
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.