Line up five normal Dino gates (stone, since they can damage wood), opening to opening, then lure it in with a Petra and slip out through the gaps. Run back around and close the gate, and it’s a fairly easy game 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.