At their next appearance both men appear via audio-visual link from Mt Eden Prison.
All charges have a maximum penalty of life imprisonment.
A statement from Customs said Koeman, who is from Thailand, flew to New Zealand from Chile on Sunday morning. He had travelled from Thailand to Brazil for a day and then spent a week in Bolivia.
It is alleged he was carrying a soft travel pillow containing 98 packages of cocaine when he arrived in New Zealand.
An X-ray of Koeman revealed two more pellets inside him, Customs alleged.
They were recovered using Customs' new "drug loo", a portable device that automatically collects and cleans the pellets and then puts them into an evidence container.
Thackray, Koeman's alleged accomplice, was arrested by the Organised Financial Crime Agency of New Zealand.
The pair's arrests come a week after a 72-year-old US citizen was charged with importing about 6.2kg of methamphetamine worth between $3 million and $6 million late last year.