Four-year-old Evelyn Greenup, Clinton Speedy-Duroux, 16, and Colleen Walker-Craig, 16, disappeared from the northern NSW town over a five-month period from September 1990.

An application to retry the man suspected of killing the children was rejected in 2018.

NSW Attorney-General Mark Speakman on Wednesday informed the families the government wouldn't support two proposals to change double jeopardy laws and potentially facilitate a retrial.

Mr Speakman said the double jeopardy rule was a fundamental principle of criminal justice systems that prevented the retrial of someone after a valid acquittal.

"I know this is a devastating blow to families who do not deserve this, to families who have lost their children to a murderer that has never been brought to account," Mr Speakman told reporters in Sydney.

Gavin Stanbrook, Colleen's cousin, said his family was "outraged" and "absolutely disgusted" by the news.

"It's deeply distressing and deeply upsetting that we have to deal with another kick in the guts from the state in a situation where three Aboriginal children have been murdered," Mr Stanbrook told reporters.

He vowed to keep hope and rely on his family and community as they continued fighting for justice.

"The fight is definitely not over," Mr Stanbrook said.

The government and NSW Police on Wednesday also announced a one million dollar reward for information leading to a conviction over the children's deaths.

Mr Stanbrook said it wasn't much consolation, with his family confident they could get justice based on the evidence they have.

"We had a quarter of a million dollars previously and unfortunately we never saw any results out of that," he said.

"Going forward, I think, what needs to be done is we need that legislation changed. That is the barrier to justice."

The suspected murderer, who cannot be named for legal reasons, was acquitted of Clinton's murder in 1994 and of Evelyn's in 2006.

The government unsuccessfully argued in the NSW Court of Criminal Appeal that there was fresh and compelling evidence to justify overturning the acquittals and proceeding with a single trial on three murder charges.

The High Court refused to grant special leave to appeal the decision, before Greens MP David Shoebridge responded with a bill seeking to change double jeopardy laws.

However, a NSW upper house inquiry found the bill would impact on too many unrelated parts of the criminal justice system and should not proceed.

Mr Speakman on Wednesday said he couldn't support Mr Shoebridge's model or an alternative by the Jumbunna Institute for Indigenous Education and Research.

"This is not about keeping guilty people out of jail, this is about protecting the innocent when they have the full might of the state against them," he said.

"It's also making sure we have finality in litigation."

Mr Speakman also considered the prospects of any retrial application in the Bowraville case, concluding that an application on either model would fail.

Mr Shoebridge said he would be working with legal experts and talking with the families about their next steps.

"Maybe it's civil litigation, maybe it's a demand for ex-gratia payments from the state government, maybe it's a formal state apology, but any one of those won't answer the core demand for justice," the Greens MP told reporters.

Australian Associated Press