Anthony, I've added all the sources I gave you the last time you asked about this couple onto Cornelius' profile.
This includes the birth of son John in 1915, which is from Irish Genealogy.
Of the names you mention, only Patricia's is on the gravestone, going by the image on FAG. The others are given in the FAG entry only. There is also a family on a tree on Ancestry that has the same offspring with the same dates.
If you look at the death record I added to that profile you can see evidence of another son who I will not otherwise reference as he may be living but there is a source for his birth. The birth location for Cornelius is incorrect on the FAG entry (based on his birth registration and as previously advised when you last asked about this family) and I have updated this on the profile.
Son James is the witness to Catherine/Kathleen Carroll's passing in 1962. I have added this source to her profile.
I am not sure how you are searching on Irish Genealogy but given the dates for the deaths are on the gravestone they should be easy for you to have found.
There are various Patricia Carrolls whose birth is registered in Dublin but the mother's maiden name is not recorded on these. There is also a Mary Carroll (assuming May is a contraction). John's is the only birth record that appears to be on Irish Genealogy (i.e. before 1917).
Have you tried a trial or limited subscription to Ancestry to help your research and/or asking the people on their with these people in their family trees?
