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I was unable to find Michael & Rose's marriage or baptism records on www.rootsireland.ie/ but did find 3 of the children including Sara:
Name:Patrick MorinDate of Birth:
Date of Baptism:17-Feb-1844Address:CarrahParish/District:Islandeady RC parishGender:MaleCountyCo. Mayo
Denomination:Roman Catholic
Father:Michael MorinMother:Rose NeedamOccupation:
Sponsor 1 /
Informant 1:John Mcdonald Sponsor 2 /
Informant 2:Anne Needam
Name:John MoranDate of Birth:
Date of Baptism:02-Feb-1848Address:N. L.Parish/District:Islandeady RC parishGender:MaleCountyCo. Mayo
Denomination:Roman Catholic
Father:Michael MoranMother:Rose NeedomOccupation:
Sponsor 1 /
Informant 1:John Callaghan Sponsor 2 /
Informant 2:Sabina Needom
Name:Saragh MoranDate of Birth:
Date of Baptism:31-Jan-1851Address:Not RecordedParish/District:Islandeady RC parishGender:FemaleCountyCo. Mayo
Denomination:Roman Catholic
Father:Michael MoranMother:Rose NeedhamOccupation:
Sponsor 1 /
Informant 1:Bridget Needham
The Tithe Applotments (free at http://titheapplotmentbooks.nationalarchives.ie/) have 2 Thomas Needhams & 8 Morans in Islandeady in 1833
As they were R C according to the above records, you may want to try the the National Library of Ireland's R C registers (free at https://registers.nli.ie) as they have Islandeady Marriages 1839 to 1880
Col Cafferky
Achill Parish