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I searched the subscription site Roots Ireland and located seven baptismal records for children of Martin Flynn and Catherine Crotty: Denis 1826 Mary 1828 John 1831 Biddy 1833 Patrick 1835 Thomas 1838 Catherine 1845. I did not find a record for Martin.The oldest four were baptized in Newcastle parish and the younger three in Clonea. Here is a link to the parish register for Clonea https://registers.nli.ie/parishes/1115 Maybe you can locate Martin's record.
From the 1850 Griffiths Valuation head of household listing, it appears the family lived in Clonea townland in Mother civil parish.
The parents were married in St. Mary's parish in Waterford city.
Date of Marriage:06-Feb-1825
Parish / District:St Mary's Parish