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Ballynona North townland is in Dungourney civil parish
I located this 1820 baptismal record for a Michael Mulerick in Midleton RC parish just to the north of Cloyne RC parish.
Name:Michael MulerickDate of Birth:
Date of Baptism:15-Feb-1820Address:
Father:William MulerickMother:Mary BarryOccupation:
There were apparent siblings Ellen 1821 William 1823 Mary 1826 Catherine 1839 in Midleton according to Roots Ireland. Very long gap between Mary and Catherine. You may want to scan the Midleton parish register http://registers.nli.ie/parishes/0079
The RC parish corresponding to Dungourney civil parish would be Imogeela, however, records for that parish start in 1833 so if Margaret was baptized in that parish, records would not be available.