One of his biographies says your grandfather was born in Bandon so this could be his birth registration,
John Ring
Registered 1876
Registration district, Bandon
vol 20 page -4
FHL Film number 101053
If you are wanting to follow your grandfather's family further back you will need to first need to find out his father's name and occupation from the marriage certificate which will lead to his birth certificate which will give both his father's name and his mother's maiden name.
There is a public tree on ancestry which has John's wife as Esther Christina Morrissey and children for Esther and John as Ellen 1910, Sarah Teresa born Limerick 1911 – 1990, Martin J 1912 – 1979 died South Africa Esther Josephine 1914 – 1915, John 1924 – 1979 died in Spain, Thomas Alphonsus 1926 – 2013, Clement M 1928 – 2005 died Eessex.
Esther J and Martin J both born in England mother/s maiden name Morrissey.
Do any of these names sound familiar?
I have enjoyed reading about the history of the Dublin Fusiliers whilst doing a little searching.

Christina