Hi Sonia
I think I have found your Grandfathers baptism record and a number of siblings all born in Cordal, Co. Kerry. If you go to this website http://churchrecords.irishgenealogy.ie/ and search for David O'Connell in Kerry the results will include nine children born between 1871 and 1892 to David O'Connell and Mary Leahy. Use the 'Additional Name' search box to narrow down the search by typing in Mary Leahy. I am fairly confident this is your family - but not certain. There is a Patrick born 06/09/1884 which ties in roughly with the other records for your Granddad. To confirm this is the correct family we would need some more details.
You said in a previous post that your Grandmother was pregnant at the time of her husbands death in 1914 and that she already had your dad and his sister Catherine so I did a search for a child born in 1914/15 surname O'Connell, mothers name Byrne and one result came up in Camberwell, London: Patrick J O'Connell, (m) Byrne, Jun Qtr 1915, v1d page 1679. I wonder are you 100% sure of birth dates etc. or could this record from 1915 be your father?
To confirm any/all of the above it would help to have some more information if possible. Do you have any other dates (deaths etc.) that can give further information such as ages? I am thinking of your dad, his parents and his siblings (hope that's not insensitive). If there are any details you don't want to post here but are prepared to share you can always email me so it's not online for the whole world to see. I know sometimes people don't want to put their personal details on here for everyone to see.
I also found a record for your Grandad on the 1911 UK Census. He was in the Cheslea Barracks in London, his age is 24 (not correct), he is married and born in Castleisland Kerry. As he was in Barracks his wife and children were elsewhere but Ireland or England? You might consider obtaining your Grandfathers service records as they might provide more information.
I hope I've been of help and would be happy to help some more if I can.
All the best.
Linda