Have you any dating / ages for these folks?
The reason I ask is that a search of the RootsIreland website index brings back a church marriage in 1813 of John Cahill to a Catherine Harney, the "parish/district" is Carrick-on-Suir RC parish.
While I can see no baptisms for an Edmond/Edmund or Joseph Cahill, searching the RootsIreland index using the given parents' names brings back a hit for a Michael Cahill, baptised in 1816, again the "parish/district" is given as Carrick-on-Suir RC parish.
The content for both records is pay to view, though I would caution that for this era, the content might not reveal much more. In addition, it has to be said that the surnames Cahill and Harney for that part of the world are not exactly rare.