The request was made by the Archbishop of Cashel and Emly, Rev Dermot Clifford.
The original fund was set up five years ago, but it is dwindling.
Parish priests have been asked to give 60 euros and curates, 50 euros.
Gary O'Sullivan, editor of the Irish Catholic newspaper, said the dioceses were running out of money.
"This is not the first diocese to show signs of difficulty in this area," he said. "They are going back to priests again and again looking for money and priests are on very low salaries. A lot of priests are quite angry about their financial situation."
Mr O'Sullivan said that parishioners saw it as a problem for the hierarchy in the Catholic Church.
But he felt the issue needed to be debated by the laity within the Church.
In a statement, the diocese said the request had stemmed from a recent meeting of the diocese's Council of Priests, where it was proposed that the Archbishop make a renewed appeal to priests asking them to help restore the fund.
The statement did not state whether the fund had been used to pay settlements to victims of clerical sexual abuse in the Cashel and Emly diocese.
The fund was first put in place five years ago to assist in covering the diocese's costs arising from the investigations into clerical sexual abuse.
The diocese said no other details on the cost of child protection would be forthcoming.