Lee and Robert Firkins were found guilty in 2005 of murdering Graham and Carol Fisher at the couple's petrol station near Wadebridge.
Solicitors said DNA from the Fishers' bungalow could show other people, who may have been responsible for the killings, were there.
Their submissions are being examined by the Criminal Cases Review Commission.
More on the petrol station murder, and other Cornwall news
No physical evidence was found to link the brothers to the crime scene, where the couple were shot repeatedly after being bludgeoned with a sledgehammer.
The Firkins are currently serving life sentences for the 2003 murders.
Jane Hickman, who represents Lee Firkins, said that since the murders, the science of DNA had "advanced enormously", and that the number of people in the database had doubled.
She said fingerprints and palm prints from inside the house that had previously not been matched to anyone may now be identified.
She said the prints may be a "game changer" in the case.
The Criminal Cases Review Commission (CCRC) has provisionally decided against sending the case to the Court of Appeal after a previous challenge to the Firkins' convictions.
That related to the reliability of a key witness, and was lodged almost two years ago.
If the CCRC agrees to the latest request, and new evidence is found, the case could go to the Court of Appeal.
The commission said: "We received submissions relating to forensics in this case - we are considering those at the moment."
Lawyers for two brothers convicted of murdering a Cornish couple believe DNA evidence could be used to clear them.