In the Griffith Valuation there was only one family Hourihane in Co Cork, Timothy in Reen Myross. But before you get too excited, Hourihane strokes me as a name with a number of alternative spellings.
Hourahane Jeremiah in Cousane Kilmocomoge and Timothy in Kilnagospagh Caheragh.
Lots of Hourahan in Kilgarriff, Ightermurragh, Fanlobbus, Kilmeen, Kilmichael, Kilmocomoge, Dromdaleague, Dangandonovan, Creagh, Caheragh, Kilmurry, Shandrum,Skull, Youghal, Templemartin, St Annes Shandon, Brigown, Ballyoughtera, Ballymodan and Kinneigh.
Most in Cahergah.
Some of these are in the diocese of Cloyne so the catholic (were they catholic?) records are closed to researchers and you have to pay Mallow Heritage centre for a search of their records. May be worth a try.
The others are the Diocese of Cork and Ross and need to be searched individually.
Kate