Catholicism in Rhode Island: The Formative Era, by Patrick T. Conley & Matthew J. Smith, insightful text and very good illustrations.
Catholicism in Rhode Island, Vol. 1, by Robert W. Hayman is a tremendous source for both history and sources. It never leaves my desk and is consulted frequently.
Irish Titan, Irish Toilers, by Scott Molloy tells the story of Rhode Island's most successful 19th century Irish immigrant, with useful (for my purposes) chapters on the background in Ireland and the early years in RI.
Rhode Island Historical Society. Old Stone Bank records offer insight into Irish immigrants records from the 1840s to 1890s.
Providence City Archives. Official forms, letters, listings detail individual lives of Irish American citizens from 1830s to 1860s. Violations, arrests, charity, warning out records and much much more.
Saints Peter & Paul Cathedral baptism and marriage records, as well as those in other churches.
Other Websites
Civil War Sources
Civil War Sources
Ancestry.com. Census Records, City Directories, Legal Documents & More. Essential.