Do you have marriage or death certs for Dominic ?
The US versions of these sometimes give details that might help your search - e.g. names of parents etc.
To check if parish records are available you usually require a more detailed location - e.g. the name of the town, townland or parish your Rogers family lived, also the denomination of the family.
see : http://www.genealogybranches.com/irish.html
(A Genealogy Guide for Irish-Americans - genealogybranches.com)