They contain the bodies of former residents of the Bethany Home in Rathgar and date from 75 years ago.
A group of survivors, who say they suffered gross neglect there, are demanding access to the State's redress scheme, which applies to similar institutions.
Bethany was a combined maternity and children's home and a place of detention for women convicts.
According to recently-discovered records, the infant-residents were buried in Mount Jerome Cemetery between 1935 and 1936.
On average, two died each month out of 19 babies.
Researcher Niall Meehan has also established the names of all 40 babies in and around two adjoining common graves.
Derek Leinster, who spent his first four years in Bethany, will convene the home's first survivors' group at the burial site next Wednesday.
He says he and other residents were grossly neglected and still suffer poor health as a result.
He also says the State regulated Bethany and should apply its redress scheme to its survivors.
A spokesman for the Church of Ireland agreed.
He said the home was run by independent trustees drawn from the Protestant community at large.
He called the deaths 'tragic'.
