I checked the list of priests, but it only includes priests currently serving, not deceased priests.The Cemetery Office might have something on the priests.So should the Archives.The Archdiocese probably had a standard biography that it gave to the newspapers whenever a priest transferred or had an important anniversary of his ordination.Those standard biographies usually included the parents' names. The Archdiocese's newspaper is The Pilot.They probably have some of those announcements in their own archives, too.You will want early announcements, because the parents' names are more relevant when a priest is younger.The Archdiocese has a lot of information, including parents' names, on the priests in their personnel folder, just like a corporation.
Maiden names are on birth certificats, and also on baptismal certificates of the woman's children.They're also on marriage documents, both Church and public.And they're on Social Security records, including the Social Security records of the woman's children.(They have to list their parents' names.)
Be sure to read the Archdiocese of Boston's Genealogy Services page.It gives what can be provided, how long it takes (up to 3 months due to personnel shortages), and what information you need to provide. Sincerely, Kate