In its letter, the Presbyterian Church has urged MLAs not to support the motion.
The two MLAs distinguish themselves from Alliance by pointing out they are pro-Union and pro-opposition.
Many MLAs spoke against the staging of coursing events where muzzled greyhounds race after a hare.
The two MLAs unveiled a joint amendment to the Criminal Justice Bill on Wednesday.
The amendment to the Criminal Justice Bill was jointly proposed by two DUP and SDLP MLAs.
William Higgins, of RBS, and Ulster Bank's head of retail banking, Stephen Cruise, also appeared before MLAs.
The amendment was proposed by two Ulster Unionist MLAs and was passed by 23 votes to 18.
Mervyn Storey made his comments as Department of Education and exams body officials faced questions from MLAs.
He was particularly critical of Sinn Fein describing its MLAs as "the economic illiterates of this assembly".
Mr Harte urged all MLAs opposed to the move to reconsider their position ahead of next week's vote.
BBC: Tyrone GAA manager Mickey Harte in abortion appeal to MLAs
That straight majority, however, did not count, because the amendment did not win enough support from nationalist MLAs.
Sinn Fein, however, joined by two MLAs from Alliance and the Green Party, managed to block the move.
The MLAS are to seek a meeting with the Further Education Minister and the college's Board of Governors.
With boundary changes and, perhaps, fewer MLAs per seat, Stormont will be a smaller legislature in the future.
Ordinarily MLAs would have a breathing space around now, with the marching season over, to revisit their proposals.
Mr Lutton's candidacy caused controversy within the UUP, resulting in the lost of two of its high profile MLAs.
The Alliance Party's Chris Lyttle said they supported cutting the number of MLAs.
Lord Empey of the UUP was unhappy that MLAs had only ten minutes each to speak in this important debate.
Since taking over, Mr Nesbitt has also disciplined two other high profile UUP MLAs - John McCallister and Basil McCrea.
But, in the interests of a "coherent" approach, MLAS were told the UK government now wishes to rectify the matter.
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Members of a Stormont committee have clashed over how many MLAs go to Washington for St Patrick's Day at taxpayers' expense.
The SDLP's Dominic Bradley said there were deep sensitivities around the motion and that some MLAs had served in the UDR.
The Foyle MP Mark Durkan and all six local MLAs have asked Further Education Minister Stephen Farry to intervene in the dispute.
They will not be MPs, MEPs, MSPs, MLAs, AMs, mayors or councillors.
He said MLAs should take a 15% pay cut and this should also apply to the top ranks of the civil service.
Within seconds another pedestrian approached to shake the MLAs by the hands.
Mr Poots told MLAs he would encourage Year 9 schoolgirls to take advantage of a vaccine to protect themselves against cervical cancer.
Mr Attwood and department officials also briefed MLAs on a planning application for a biomass-fuelled power plant at Glenavy in County Antrim.
Amid heated exchanges at a Stormont committee hearing, MLAs questioned whether social workers and doctors had got it right when giving evidence.
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