Your going to want your trap near the plains by green on, Have 5 Dino gateways lined up next to each other with 2 Dino gates on each end. Have each space big enough to just barely fit a ptera thru. After that have one gate opened and one closed and agro a griffin. Lead it thru the trap and fly thru the top then while it's still agro on the ptera on the closed gate side, close the other gate and tranq!
Before you all go naming your griffins "Buckbeak" lemme lay some mythology on ya. Buckbeak from Harry Potter was actually a hippogriff which is a horse combined with a eagle. A griffin is a lion combined with an eagle. Just keep this in mind before going on a Buckbeak naming spree.