To tame a Kairuku a good method is to knock them out with tranqualising arrows/darts or slingshot. But both of them are able to kill them too, so you always need to be careful and watch the Kairuku. Watch Dinosaurs trough the Spyglass, will show u the Dino's Level and below the Level, their Health. The Kairuku is non-aggressive and will flee once u start to attack him. If u attack a Kairuku with other Kairukus around, they will begin to flee as well.
Once knocked out you need to feed him with raw meat or raw prime meat. Raw Prime Meat will tame it faster. In most cases there are no narcotics or Narcoberries needed, but it is always wise to take some narcotics/Narcoberries with u, just in case.
They are so cute! I tamed one today and I named it Karri. She is a juvenile and very weak but still cute. If you kill baby or juvenile kairukus on purpose. I will find and burn your base in multiplayer.
DO NOT MAKE THE SAME MISTAKE AS I DID. I hit headshots when trying to knock this oversized penguin out, and it died... Just remember to go for the body, and only use tranq DARTs, otherwise it will die, please share to others