Welcome to Rootschat. Irish research is very difficult without an exact place of residence known. Civil registration of births in Ireland started 1864 so it's possible that James (born about 1865- probably earlier based on siblings birthdates) had no birth certificate. However, IGI (
www.familysearch.org) lists several other children for Denis Flaherty and Ellen Danaher:
1. John born 16 Feb.1865 Ardagh and Athea district, Co, Limerick (page 0633 in civil register)
2. Ellen born 11 Dec.1866 Ardagh and Athea district, Co. Limerick (page 0531 in civil register)
3. Patrick born 21 May 1868 Co.Limerick
4. William born 15 Apr.1872 Co.Limerick