Tame on Ragnarok during Evolution event, use an Equus to get Narcoberries for the Tranq Arrows, get at least 10, find a Ptera, bola it and knock it out, and then find an Ovis and harvest the Mutton and place it in a herbivore to preserve it, or you can get kibble with a dodo farm because of the Rockarrot, so then come back to it, and it should be waking up, let it wake up, and then re-knock it out with a bola and tranqs, place in your food and then you have a Pteranodon that won’t die in 1 hit and won’t have to land every second. Happy hunting!
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!