Build a taming pen from 5 or 6 Dino gateways and two gates. Space them roughly equally apart leaving enough space to run in-between the gateways to get in and out, but not so much space that your tame can escape.
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.