The chief executive of the Trust set out its position in documents which were obtained by patients' families under the Freedom of Information Act.
The health minister is due to announce the outcome of a consultation on the service at the Children's Hospital.
It was put under consideration after it was deemed unsustainable due to the numbers of patients it deals with - around 90 per year.
The Department of Health is consulting on options, including whether to treat patients in Dublin or in England.
"We believe that the best option for the provision of a safe and sustainable service for children with congenital cardiac conditions is for the development of a network arrangement with Our Lady's Hospital in Dublin where surgery, interventional and diagnostic catheterizations are undertaken in Dublin for Belfast patients by Belfast and Dublin clinical staff," the Trust document stated.
The Trust supported a gradual transition to Dublin that would take "preferably" no longer than a year.
"The resulting combined all Ireland surgical service would have a case load of at least 650 surgical patients per year, easily meeting the minimum number of 400 paediatric surgical procedures per annum," the document said.
The Trust is confident that a sustainable service arrangement can be delivered on an all-Ireland basis for the majority of the paediatric service.
The Children's Heartbeat Trust has been campaigning to keep services at the Royal open.
Its chairman, retired paediatric cardiologist Dr Connor Mullholland, said the Trust's conclusion is "ill-informed and ill-advised" and that children's lives may potentially be put at risk.
"It does not, at this point, support the evidence from several reviews of the cardiac surgery within the Children's Hospital," he said.
"At the moment, there are newborn babies who get a procedure carried out within hours of birth in the children's hospital, or in the maternity hospital , but who will under these circumstances be taken to another centre and certainly the risks are increased as a consequence."
He said the response from parents' groups has been enormous in their opposition to the move.
He said that he had also heard from staff at the Royal Hospital who were opposed to the removal of the service.
He said: "They really have said that if a speciality that deals with a hundred children a year is vulnerable, then what could be done to other small but important specialties in the Children's Hospital as a consequence?"
Aidan Kearney, whose son Ben was referred to the Children's Hospital in Belfast, said he received the best of care.
He said that Ben has had to go back to the ward for follow up treatments, which Mr Kearney said may not be available in Belfast if the changes go through.
"It's been very hard since we first found out that Ben was diagnosed with a CHD (congenital heart defect) two years ago.
"We have been lucky in that the procedures that Ben has undertaken so far have been able to be carried out in Belfast.
But he said that he has concerns about the future as Ben will require further surgery.
"We have a very good support network in Belfast, a very good support network, we have family and friends close by who would look after our other two boys," he said.
"However, if these services were taken to Dublin or England, with an emergency procedure there's no guarantee that you would get to the hospital in time.
"Also the support network just wouldn't be there to support our family. We wouldn't see our other two children when we were away."
A Belfast Trust spokesperson has said that no decisions have been made in relation to the future configuration of the paediatric cardiology services.
"The HSCB have approved a framework for the commissioning of paediatric cardiac surgery and interventional cardiology for children in Northern Ireland," they said.
"This framework has been sent to the Minister of Health for his consideration. The Trust awaits the outcome of this review."