William,
I can find no more definite records at all. I see on ANcestry the marriage but it is just the list, you can order up the actual certificate or the extract which is cheaper and that should record the father at least and possibly if he is living or dead and sometimes if you contact the church they may have more information if they will supply it, again it is an idea to make a donation etc for their time.
I checked the census for both 1901 and 1911 for any Bennett in Artramon, there was only one family and they were too old to be having a child in 1901 and he was a tailor, she was dead in 1911 and was only 50 in 1901, one other Bennett family of 2 sisters there, it is such a precise address to have it must be correct. I looked for a Sidney Bennett in all the BMDs available to 1950 from 1845 when civil records for Protestan marriages began. There was none.
I found a Sidney Bennett aged 5 in the 1901 census and this may be interesting or not, there was no head of house in the Curragh in Kildare but the wife listed herself as wife to head indicating he was alive somewhere, it was a military house and she is Gertrude, they listed themselves as Church of England, there are a number of Gertrudes married to Bennetts in England so I cannot find the correct one but none to a Sidney. The wife Gertrude was only 32 in 1901 and had a 13 year old child so married at 19 or so. I tried one or two children on Ancestry with unusual names to no avail, if you think there is any point in pursueing this the British Library may be your first port of call, I wonder if that child I found in the 1911 census in Wexford is her though listed I think as Church of Ireland (Irish Anglican church). If May was born in the military complex she may be registered there rather than in a parish etc. Otherwise I am at a loss here.
http://census.nationalarchives.ie/pages/1901/Kildare/Ballysax_East/Curragh__Part_of/1442173/ Form B1 says all buildings are property of War Department, all Bennetts listed born in England.
Good Luck
Pat