Just make a 3x3x3 made of stone pillars leaving one unplaced. Next use a ptera and aggro the griffin you should be able to slip through the gap. Next block the entrance with a spare pillar or two. Then voila. (Don't forget ceilings too!)
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.