If you think u are fast enough: it also spawns in the pit at the green obelisk. If you shoot the first tranq arrow with a good crossbow (~180%) than it has to fly al the way up and gives you time to shoot another few arrows (maybe preload some other bow so you can immedately switch) I tamed a 128 and a 116 this way although it might take a while before you find a tapejara there.
Extremely difficult to tame. Best options are to bola it, and then use a longneck rifle with tranq darts. Otherwise trying to get it to fly into the side of a cliff and get stuff is the other option for a solo tame.
Since the new update, rare flowers make dinos aggro on to you, you can use this on a tapejara and it will follow you to a trap you've built. Just remember that each flower gives only 10 seconds of that debuff so if the bird is far away from your trap, you have to use it frequently while coming back. Also, if you need it to follow you after you've gotten off your dino, you need to eat another rare flower so that it can agro on to you once again.