EASIEST WAY TO TAME AT ANY LEVEL:
Stock up on trans, 4 - 5 per bird, wait for it to land, walk an aim-able distance away, FIRE AWAY, when it comes close, run towards it while flanking from the side and from behind as it passes, you WILL take a foot or two, so be prepared to have SOME food handy for yourself.
They stay tranqed for a little over 30 minutes. Use that time to starve them whil you hunt some predator or big game to get some prime and VOILA!
I solo play and just tamed 5 Argen in one go. I am going to paint them blue and call them The Blue Angles. 😉
An argentavis can't fit through a ceiling with one tile missing, but a pteranadon or lymantria can. Build a trap with one corner ceiling missing, aggro the argentavis, fly in one side and out the missing ceiling tile, and land. Dismount, run around, and close the entry door. Tame safely at your leisure.