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If you don't have the image of the marriage record in Moycullen, here is a link http://registers.nli.ie/registers/vtls000634195#page/59/mode/1up
I checked on Roots Ireland and they have records starting in 1848 for Moycullen RC but there is an annotation that earlier records back to 1786 are in the National Library in Dublin.
I did not find any baptismal records on Roots Ireland for children of Bartly Noone and a mother with the surname Griffin. Did they emigrate after the marriage.
We can look for records for others ancestors if you provide names and approximate year of birth. Parents names would be a big help. We are constrained that many parishes in the West of Ireland have records starting 1850 or later.
You can also enter your family surnames in our search box at the top of our main message board. Possibly someone with similar connections posted an earlier message.
Have you considered autosomal DNA testing?