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I did a quick check of Roots Ireland for Catherine Monaghan marriages to a Barrett or Joyce in Mayo and got no record. The Belmullet RC parish records start in 1836 for marriages and 1841 for baptisms. Unfortunately, there is a gap in marriage records from 1845-1858 http://registers.nli.ie/parishes/0742 which likely covers the period where your ancestors married. The Kilmore Erris and Kilcommon Erris records start around 1860.
I was also unsuccessful in finding baptismal records for any children of the two couples.
Have you considered autosomal DNA testing?