A good way to tame is get a crappy pter, fly it in a trap made of door frames and a dino gate. Run out the doorframe, shut the door while it kills ur pter, then knock out when ur pter dies. Have an argy nearby for defense/ to help if anything goes wrong, and just so you have a mount to escape on if needed.
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.
I recommend using a trap (unless you already have a grif then you can just tranq it in the air). I found that 7 dinosaur gates worked the best. Also I found it easier to have a friend on so they can lead it towards you in the trap. And then you just have to agro it somehow. Also make sure your tames are on passive in case it hits you.