The pair were remanded in custody and will next appear in Taupo District Court on September 10.
Moko's aunt posted a tribute to him on Facebook last night.
"He's gone, he's actually gone, feeling like sh*t," she wrote.
"I'm so sorry I wasn't there wen u needed someone to be there... Love and missing u like crazy. No matter how hard I cry seems that I still have way more tears.
"My eyes are burning because of how much I love yuh and I no its probably nothing compared to wat u had to through but no more pain my baby."
She said Moko's death "has ripped up our hearts to pieces"
"This pain can never be healed ever. Nobody could ever take away the love that we all had/have for u," she wrote.
She said she had never seen Moko's father cry before, but he was distraught.
"My world has just shattered. Today is one of the worst days of my life. At 3-years-old u have been taken away... u have been taken way too early. Words cannot express how I feel and I just cannot imagine how ur dad is feeling."
The investigation into how Moko died was ongoing, police said.
A post-mortem examination began yesterday in Auckland and would continue today, police said.
Police said they would also carry out a forensic examination of a house on Marshall Ave in Taupo.
Detective Senior Sergeant Lew Warner yesterday said the investigation would rely "heavily" on information and advice from medical experts.
Police would not comment on the nature of the injuries.
A neighbour said the first she knew something was wrong was when she arrived home on Monday and an ambulance was outside. She said it was only yesterday morning that she heard about the death.
The neighbour, who did not want to be named, said the woman living at the address seemed "lovely" but was a very private person.
The dead child had at least one older sibling who attended the nearby school.
A staff member turned up at the address yesterday looking visibly upset.
Other children from the address are currently in the care of CYF pending the outcome of the investigation.
An email was sent to Taupo District councillors yesterday morning advising them of the investigation.
Mayor David Trewavas yesterday said he had also had a briefing with police about the incident.
"This is obviously very devastating for everyone, for the whole community. It's a sad, sad day in Taupo today.
"This was a reasonably good area in town, in close proximity of a very good school ... it would be devastating for the neighbours as well."
Councillor Anna Park said the new was "heartbreaking" and beyond comprehension.
Anyone with any information was asked to contact Taupo Police on 07 378 6060 or Crimestoppers, anonymously, on 0800 555 111.
