Hello Paul,
It's great to see that you are researching your roots! :)
In 1864 civil registration was introduced in Ireland, which is when we started seeing the formal registration of births, marriages, adoptions and deaths. As Brian already mentioned above, in this case you can apply for a copy of his birth certificate via the General Register Office of Ireland (
GRO), which is where all of these records are being kept.
We hope you'll receive an answer from them soon, and please don't hesitate to reach out here if you have any other questions!