Stone, 53, a former Ulster Defense Association member, was convicted at Belfast Crown Court of the incident at Stormont in November 2006, The Times of London reported Friday.
He entered the parliament building armed with explosives and weapons while the assembly was in session.
Stone, who had served a prison sentence for killing three mourners at the IRA funeral in West Belfast, claimed that his actions were "performance art."
The judge rejected the argument, the newspaper reported.
"I am satisfied that Mr. Stone went to Stormont to try and murder the two Sinn Fein leaders on November 24, 2006," the judge said.
Stone was also convicted on seven other counts, including possession of nail bombs, three knives and causing damage to the Stormont building.