So it looks like a dead end. ..why would the marriage not be registered, I thought all marriages had to be post 1864?
From what I have found some priests, who acted also as registrars hence only one ceremony in Ireland, did not always register all of their civil records. Sometimes that coincides with a change in priest in a parish. I have found several church marriages that are not on the civil register
FTR
In case you had not come across this record
It is not referred to in the other topic
William CARROLL and Mary Anne BENSON had a son Thomas Christopher on Jun 02 1913
LINK #31
He died on Dec 26 1913 aged 6 months
LINK #399