If that is typo for thomas born 1876, and the real date is 1846, then he and his family Mary and two daughters could be living in 1881 at Dale Terrace, Crook & Billy Row, Durham, England see familysearch.com. The entry reference was under Thomas Carroll and Ireland and then it is a copyrighted census item.
Hoping this is useful and not a red herring
Ros Davies Co Down webite doesnt appear to include Carrolls and might be an error in her filing. Try emerald ancestors, ancestryireland and perhaps more familysearch references