Kunaqoro is charged with importing about 14kg of P and Molidegei with importing about 1.05kg into the country.
The pair are also charged with possessing these amounts of the drug for supply.
The charges carry a maximum penalty of life imprisonment.
Customs said the 34kg of methamphetamine seized is worth up to $17m.
The defendants, who appeared in Tauranga District Court on Wednesday, were both remanded in custody to next appear in the same court on December 12.
They are yet to plead.
Customs investigations manager Bruce Berry said the seizure was a reminder that Customs was active in seaports across the country.
"This vessel was identified as posing a potential risk before it arrived in New Zealand, and the seizure is the result of some very good work by Customs frontline officers in Tauranga - one of the main shipping hubs into New Zealand."
A Customs spokesman confirmed the Southern Moana is currently in Auckland and the ship and its other crew were expected to leave the country in a few days.