A common trap for Arial creatures in general is that you craft about 4 stone dino gateways, then place them in front of each other (so that it's just a straight row of gateways). The ones on the outside place a little farther away so that you can walk through the sides, then have gates on the outer gatways having one of them open so that the bird can fly in, once you find the bird of choice, kite it into the trap, go through the side space that is larger on the end, and quickly go round to the open gate to close it and now you have easy tame stuck inside your trap. (You can modify this if you want, particularly the size of the gateways for the bigger creatures and it can be used for terrestrial creatures too if you want)

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