Thirty four fresh claims have been made since a safeguarding review seven years ago.
Over 130 allegations of child sexual abuse against its members have reportedly been received by the Irish wing of the St. John of God order which ran special schools in Ireland.
The Sunday Times says 34 fresh claims of abuse have been made since a safeguarding review was carried out in 2015.
The newspaper says the religious order was aware of 97 allegations of child sexual abuse at the time of the review and 12 civil cases are being taken against the order for child sexual abuse in school.
No members of the order in Ireland have been convicted of child sexual abuse or placed on the sex offenders register.
According to the Sunday Times, the allegations are made against 41 congregation members and 10 of the abuse claims relate to incidents which allegedly occurred in Africa and the UK.