The group has already taken out full-page adverts in consecutive editions of the weekly Scottish Catholic Observer, the first of which led to a complaint to the Electoral Commission as it failed to state who paid for it.
The advert featured Lord John Reid, the former Labour Home Secretary, saying: "I am a proud Scot and want the best for my country. That's why I will be voting No to separation in September. A No vote is a vote to protect the best interests of Scotland and its people."
It was signed "John Reid, former Labour Cabinet Minister and Former Chair of Celtic FC".
Lord Haughey, a former director of Celtic FC, said the omission of the information on who paid for the first advert was "a mistake".
When the advert was rerun in this week's edition, it carried a statement saying it had been placed by Lord Haughey's personal charity, the City Charitable Trust.
However, the peer told the Sunday Herald this was another mix-up, and both adverts were in fact being paid for by Faith in the Union.
The group's members, who Lord Haughey refused to name, plan to take out similar adverts in the Catholic Observer up to the referendum.
Lord Haughey, 57, said the move was prompted by the Yes group Christians for Independence buying the same advertising slot two weeks ago.
He said: "I'm behind the adverts.
"One of my relations brought in a copy of the Catholic Observer which showed a full back-page advert from Christians for Independence.
"It looked like an endorsement from the Church to vote Yes.
"So because of that, which I didn't think was right, I decided to redress the balance."
He said Faith in the Union was the pro-Union equivalent of Christians for Independence, which has been bankrolled by £100,000 from Stagecoach boss Brian Souter, but unlike it, it would not register as an official campaigner, as it did not intend to spend above the £10,000 threshold. Instead, those associated with it would spend money in a rolling purchase of advertising.
He said: "I may take out some adverts, but there's other people involved in Faith in the Union who are going to step up to the plate and they will pay for the adverts themselves."
The founder and boss of Glasgow-based City Refrigeration Holdings, Haughey gave £1.3m to the Labour party between 2003 and 2012, becoming the party's biggest Scottish donor.
He was named a Labour peer in August 2013.
Since then he has given a further £48,000.
Canon Peter McBride, who describes himself as "nationalist to the hilt", said he had banned the Catholic Observer from his two parishes in Glasgow's East End because of the Reid advert.
He claimed it was "dividing the community" and wrongly mixing party politics and the Church.