Thanks for all the suggestions, I should have included a bit more info on where I have looked for information on the family.
They appear on both the 191 & 1911 census.
Both web sites, Irish Genealogy & Roots Ireland, have been searched in multiple ways.
I also have the Birth Certificate - no name for the child was inserted on the birth certificate at the time that the birth was registered by a person from the Rotunda who was 'present at the birth'.
I think the problem arises, as far as the online information is concerned, is that the 'cut-off' dates for the filming of those RC Baptism Registers that were filmed is, exactly that!
The churches referred to in my initial post can be ruled out because I have already been in touch with them and had a 'not found report' from each of them as far as the date & the parents are concerned. So it looks as if it will need to be a call/email to other likely suspects where the filming dates were before the birth in 1900 - St Agatha looks as if it might be a possibility - thanks eadaoin.
H