Besides using a tapejara, you could use a quetz catcher. You can google this for photos. Basically, if you have a quetz, or someone you know does, you can build a catcher on the back (thatch is fine). After "catching" (making it fly into the catcher) the quetz, jump off the quetz onto the platform saddle and add some walls in the open spaces (where it flew into). Then, you can shoot it with darts or arrows till it's down. Or, you can have a friend shoot at it from another bird/platform.

More Quetzal Taming & KO Tips