One thing that you could do (if your desperate) is build a tiny wood cage just big enough to fit a tapejera. Once you’ve done that find a good tapejera and eat a bunch of rare flowers. It will start to attack you (Make sure that your flying on a pteradon with good health(otherwise ground creatures will attack you)) then fly into the cage and shut the door and KO that thing.
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.