There are an estimated 20,000 children in New Zealand with at least one parent in prison.
Children of prisoners are estimated to be six or seven times more likely to become prisoners than the children of non-prisoners, without intervention.
Ms McFelin said many families would not bring their children to visit in the past, because the experience was not so practical or pleasant for families in the large visitors areas.
"These areas have not been set up for families and are not conducive to children," she says. "As it becomes known that there are facilities for children, we hope that more families will bring their young ones to spend time with their fathers and we will be able to run the sessions more frequently."
Prison manager Stu Davie said the prisoners are looking forward to Sunday's opening and "sharing time with their families'.