This is way I do , personally.

1.make atleast, 4 or 5 STONE dinosaur gates and 2 stone dinosaur gate doors

2. Make a Net launcher thing and a net projectile.

3. Make sure that you're on a tame or have on some good armor so while it's going at you, you don't die

4. Shoot the net projectile at the griffin and then place the stone gateways over (with little gaps so you can shoot but also small enough ot can't glitch through) and the put the gateway doors in.

5. I would suggest using longneck, crossbow or compound bow (if you have the m available) but a regular bow works as long as you have , I would say 20-40 TRANQ arrows.

6. Try aiming for the head so it can speed things up with 4-7 second intervals

7. MUTTON is going to be the BEST taming food once it's knocked

8. Enjoy your new griffin lol - Kameron