If you do not have a bola on you, it always work to pick up an egg and piss off the parents. That’s how I have tamed a couple of my pteras and it works surprisingly well. They don’t fly away after taking so much damage, and they don’t do a lot of damage either as long as you have armour. (It also works to make a doorless hut and punch ‘em or something)
When knocking pteranodons out, be sure to have a bola, it doesn't take many tranq arrows to knock it out. Once it is down, put spike walls up around it (with a little space so you can go in and out) so it doesn't lose taming efficiency or die.
To kill pretty much anything on these birds, tame a high level, then pump stam to 3k, then the remainder in melee. Barrel roll into alphas etc. But keep eye on Stam. Never regen Stan on ground, know your ledges!