Naupoto - a Tongan national - was also charged with conspiracy to kidnap and was remanded in custody.
Wolfgramm and Tanginoa, both of Auckland, were released on bail.
All three men are involved in premier club rugby or league.
Wolfgramm is a former Tongan league international who played at two World Cups.
Better known as Willie, the 40-year-old is also a player-coach for the Bay Roskill Vikings and is listed to play in the Auckland club final this Saturday.
Naupoto is the former manager of the Tongan rugby union team and secretary for the Tonga Rugby Union, while Tanginoa is a former Tongan union international and was signed by the Brisbane Broncos league team in 1995.
He once coached the Tongan sevens team and is now involved in the coaching set-up at Auckland club side Teachers Eastern.
The three men allegedly tried to arrange the purchase of several hundred kilograms of methamphetamine from Tonga, according to the head of the Auckland police drug squad.
Detective Inspector Bruce Good said the arrests were the result of an investigation which began in July when Naupoto arrived in New Zealand with an associate after travelling to Tonga to sample the "drugs".
The Tongan "drug syndicate" went to great lengths to convince the potential buyers in New Zealand that the product was genuine, said Mr Good.
"They made blocks to look like a [methamphetamine] stockpile then put rock salt in it. On top of the rock salt, they put a small amount of locally purchased methamphetamine," said Mr Good.
"So when [the buyers] asked for a sample, they gave them a shard of genuine ice, methamphetamine. And they knew exactly which shard was real."
By this time, police in Tonga and New Zealand were investigating the alleged conspiracy and last Friday interviewed several men in Tonga believed to be suppliers.
But police discovered that no methamphetamine actually existed.
Mr Good said the Tongan-based members of the alleged drug syndicate were in fact attempting to "scam" hundreds of thousands of dollars from Naupoto.
The Herald understands the police inquiry is now tracing the criminal network that Wolfgramm and Tanginoa were allegedly trying to supply the "methamphetamine" to.