Had a look on-line and the best I could come up with was
Michael Ahearne born 04 July 1873 son of Thomas Ahearne & Mary Fitspatrick it has them living in Waterford at the time that the only problem
You could apply to the GRO
www.groireland.ieSometimes they will do a search for you of their records for the Carrigaline area.
Did you find any Thomas Ahern in the 1901 & 1911 Census?
This is the only one I could find for the 1901 Census could not find any Thomas Ahern as a Baker
Household Number 7 District Electoral Division: BALLYGARVAN
Address: Ballygarvan Parish CARRIGALINE
County Co. Cork
First name Surname Occupation Age Relationship Denomination Origin
Thomas Ahern Farmer 50 Householder Roman Catholic Co. Cork
Thomas Ahern None 3 Son Roman Catholic Co. Cork
Margaret Ahern Scholar 15 Daughter Roman Catholic Co. Cork
John Ahern Farmer 17 Son Roman Catholic Co. Cork
Ellen Ahern Farmer 18 Daughter Roman Catholic Co. Cork
Catherine Ahern Farmer 19 Daughter Roman Catholic Co. Cork
Mary Ahern Farmer 21 Daughter Roman Catholic Co. Cork
Timothy Ahern Farmer 23 Son Roman Catholic Co. Cork
Ellen Ahern Farmer 45 Wife Roman Catholic Co. Cork
As Thomas was a baker he may appear in commerical/trade directories have you ever used these?