The family of Jason Corbett said they hope a date for Molly and Tom Martens' retrial will be set at a hearing on Friday.
And in a statement from the Limerick man's relatives, they insisted "perpetrators must pay for their crimes".
The Martens have been free for nearly a year now following their release from a North Carolina jail in April of last year.
In 2017, the daughter and father were convicted of second-degree murder for Jason's killing on August 2, 2015.
But last year, a Supreme Court quashed this and ruled that they were entitled to a retrial.
With the Covid-19 pandemic, there has been a massive backlog in the courts there.
On Friday, a hearing at the Davidson County Superior Court will take place and it is hoped a date can be set for the retrial.
On a memorial page on social media, Jason's relatives said: "At this hearing, we hope prosecutors and criminal defence attorneys for Molly and Tom Martens will announce a trial date.
"We can only hope it will be sooner rather than later. It is now approaching a full year since (they) have been released from prison.
"Enjoying their freedom in society. But for society to be just and fair, perpetrators must pay for their crimes. Not with a token sentence of mere months."
Jason's sister Tracey Corbett Lynch previously said Jason's children were prepared to give evidence in the retrial.
The now teenagers are from Jason's first marriage to Margaret Fitzpatrick, who tragically died after an asthma attack in 2006.
As part of the Martens' successful appeal, their legal teams claimed statements given by the children to social workers after their dad's murder should have been allowed as evidence.
But Tracey, who now cares for the teenagers in Limerick, claimed they had been coached and intimidated by Molly to give false information and once they came back to Ireland and away from their step-mother, they recanted those statements.
The statement added: "What followed was a disgusting smear campaign.
"Jason is gone forever and the finality of his death is the hardest cross to bear.
"(Molly and Tom) walking free makes it even more unbearable for his family.
"The punishment MUST fit the CRIME."
