In mobile, if your names last two letter and griffins last two letter is same they respect you and in mobile i knocked out it but he didnt eat the meat you must use allo kibble or griffin kibble. (please click up button for everyone see)
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.