Honestly if you find one in the air on any flyer fly high above it, whip out a crossbow and grapple to it, whistle your flyer to follow you so you don't have to find it again (or just make sure you have it done beforehand). Finally, switch to a bow or a rifle and tranq that guy and make sure you detach and pop a chute before you hit the ground. Quite possibly the wildest way to tame a Tapejara or a Quetzal.

More Tapejara Taming & KO Tips