The twins' father, Chris Kahui, was acquitted of the 2006 murders, after his legal team ran a defence implicating their mother, Macsyna King.
No one else has been charged, and police have said fresh information would be needed to restart the investigation.
Inquiry head Detective Inspector John Tims said there was "not sufficient evidence to support any prosecution of Macsyna King in relation to the twins' death".
Family First offered at $25,000 reward for information last month, and this was matched last week by Sensible Sentencing Trust supporter Michael Jacomb, taking the total to $50,000.
"There's a rule that people have a right to silence," he told the Sunday Star Times. "Well then I've got the right to put that money up to beat that silence. The country will be pleased to see a result there."
Macsyna King's half-sister Denise King said the lure of cash could persuade her siblings in the notorious "tight 12" - who had access to the three-month-old boys in their final days, but refused to co-operate with police investigations - to divulge what they knew.
"I know money says a lot. It might push people into telling the truth, saying what they know," Ms King said. "They're tight, but they're not that tight."
Since the murders, Denise King has pressured her siblings to come clean about what they know. She is critical of police efforts to resolve the case, and believes that redoubling efforts to interview family members individually could lead to a breakthrough.
