Richard McFarlane and Maureen MacLeod were part of a lengthy dispute between parliament and the IndyCamp group.
The camp was evicted in November 2016, but a series of court appeals continued afterwards, with each being rejected.
The Supreme Court said the application for the latest appeal "does not raise an arguable point of law".
This means the judgement given by the Inner House of the Court of Session in October 2016 stands.
The camp was set up on the edge of the parliamentary estate in November 2015, with the stated objective of maintaining a vigil until Scotland became independent.
The parliament's corporate body ordered them to leave, arguing that they were camping without permission, and potentially compromising the political neutrality of the parliamentary estate.
Lord Turnbull ruled against the group in the summer of 2016 after a lengthy and often colourful legal battle, and his decision was subsequently upheld by the Inner House.
The campers applied for leave to challenge that ruling in the Supreme Court, but this was also rejected, with Scottish judges saying it was not a clear matter of public importance.
Mr McFarlane - who argued repeatedly during the original case that Christ had returned to earth and had given permission for the camp to stay - submitted an application directly to the UK court, saying the group's rights to freedom of expression and freedom of assembly under the European Convention of Human Rights had been infringed.
A panel of three Supreme Court justices considered written submissions, but ruled that "permission to appeal be refused because the application does not raise an arguable point of law".
A spokesman for the Scottish Parliament said: "The SPCB welcomes today's decision of the Supreme Court, which brings this matter to a close."
Mr McFarlane and Ms MacLeod were two of nine respondents in the original case, and submitted one of four appeals heard at the Court of Session. It is not thought any of the other campers applied to the Supreme Court for a fresh appeal.
The Court of Session ruled that the campers should have to pay the costs for the case, which were estimated as running in excess of Â£128,000, but the parliament ultimately decided that pursuing them "would not be cost effective".
The Supreme Court has declined to hear an appeal from two former members of a pro-independence camp which was set up outside the Scottish Parliament.