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You likely know that Newport RC records start in 1872.
On the free site www.irishgenealogy.ie I located the 1888 marriage for Paul Moran and Fanny McManamon. I also found an 1890 birth record for a Mary Anne Moran which may be your Anne Moran.
I found the 1901 census record which showed the widower John Moran and his son John and his family in Roskeen North. I also found John Sr.'s death record in 1908. I did not locate Mary Moran's death record because there were too many Mary Moran death records in the Westport registration district prior to 1901.
I assume Paul and his family emigrated pre 1901?