Brendan McConville and John Paul Wooton were found guilty last year of the murder of Constable Carroll, which happened as the officer answered a 999 call in Craigavon in March 2009.
But the pair have since launched an appeal against the verdicts, which saw McConville handed a minimum of 25 years in prison and Wooton a minimum of 14 years.
The defence now claim a new witness has come forward who alleges the key prosecution witness in the original trial is a compulsive liar and a 'Walter Mitty' character.
There is such a high level of uncertainty as to the factual circumstances surrounding the position that we are faced with having no alternative but to adjourn this appeal.
Lord Chief Justice Sir Declan Morgan
With supporters of McConville and Wooton in the packed public gallery, a few feet from Constable Carroll's widow Kate, a defence QC further told the court that their new witness had been arrested by police last Thursday and held for two days.
Senior judges were further told that the officers forced their way into the home of the witness and warned him that he would be discredited if he went to court.
The lawyer claimed that this was an attempt by the police to sabotage the appeal by McConville, 41 and from Tullygally in Craigavon, and Wooton, 22 and from Collingdale in Lurgan.
The defence confirmed that they are to lodge a complaint with the Police Ombudsman, while letters will also be sent to the Public Prosecution Service and the Law Society.
The appeal has now been adjourned until October.