The group, Religious Abuse Truth, said it was organising a letter writing campaign in order to force Dublin auxiliary bishops Eamonn Walsh and Raymond Field from office.
Protesters are also planning a picket of the papal nuncio’s residence to protest against Rome’s decision not to allow the bishops to resign after they were named in the Murphy Report into the cover-up of clerical sex abuse.
Campaigner Kevin Flanagan said: “It’s an absolute joke.
“How could anybody be kept in their job like this. I am asking everybody to write to the two bishops and ask them to just resign themselves.
“You don’t have to do everything that you are told to do in this world. The decent and the honest thing would be for them to stand down and put their hands up and say we are resigning ourselves.”
Kevin’s brother, Mickey, was a survivor of the notorious Artane Industrial School and, according to the campaigner, drank himself to death at the age of 59 as a result of the abuse he suffered there.
Pope Benedict has refused to accept the resignations of the two auxiliary bishops who offered to step down in the wake of the Murphy Report.
Instead, Bishops Raymond Field and Eamonn Walsh will remain in their positions and are expected to be assigned new, revised responsibilities.
It remains unclear what role the two bishops will be given in their parishes.
Archbishop Diarmuid Martin told priests by letter that this week that the two men would be “available to administer confirmation in any part of the diocese in the coming year”.
It remains unclear though whether communities in south Dublin where Bishop Walsh is based and in Finglas where Bishop Field is based will have a say in how the two clerics will work.
Mr Flanagan said those who feel strongly about the issue should personally write to the two bishops involved and make their views known.
“I would ask people to say in the letter ‘do the honourable thing, hold your head up high and resign’.”
The Religious Abuse Truth group was responsible for staging an Easter Sunday protest earlier this year when 1,000 children’s shoes were tied to the railings of the Pro-Cathedral in Dublin.