Very quick way to tame these is you get them trapped start shooting them in the head with tranqs for 3x torpor then when the reach 75% torpor the will try to fly away that’s when you kill as small Dino like a dodo hold it under the argentavis until it’s torpor drains just past 75% then it will attack you harvest the dead Dino and then as fast as you can fire as many tranqs into it (helps if you have a friend or a good crossbow or longneck for high levels) and if you can knock it out with it’s healing buff still active it’s good will Dorian very fast for a quick tame.
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.