Best place to tame is the Griffin Trench on Crystal Isles, located near the Desert Wyvern Hive in the... well... desert. Argy traps work fine, remember to use double doorways instead of pillars, so much easier. Don't be me and build your trap close to the Desert Wyvern Hive. You will be surprised how far out those wyverns fly. Would recommend building the trap at the end of the Griffin Trench closest to the savanna hills with the purple crystals. Do not build on the side closest to the tropical area.
After building your trap, standard procedure, use ptero to lure nearby Griffin into trap, close the door. You can use traq arrows, but switch to darts after it starts getting bloody. Wait for four seconds in between shots to maximize efficiency. This does not apply to darts, as the dart reload animation already lasts four seconds.
You can shoot weapons and do a dive on Griffins, but they are otherwise useless. I wouldn't even recommend shooting from their backs as their body tends to get in the way.