Hi Pat,
There are 3 possible records for William on www.rootsireland.ie/:
Name:William MologhneyDate of Birth:
Date of Baptism:05-Jan-1845Address:
Parish/District:ST MARY'S CLONMELGender:
CountyCo. Waterford
Denomination:Roman Catholic
Father:William MologhneyMother:Catherine SlatteryOccupation:
Sponsor 1 /
Informant 1:James Heany Sponsor 2 /
Informant 2:Joanna Hackett
Name:William MullownyDate of Birth:
Date of Baptism:19-Jan-1845Address:
Parish/District:TRINITY WITHOUTGender:
CountyCo. Waterford
Denomination:Roman Catholic
Father:Thomas MullownyMother:Judith HonanOccupation:
Sponsor 1 /
Informant 1:Geof Prendergast Sponsor 2 /
Informant 2:B. Hogan
Name:William MolownyDate of Birth:
Date of Baptism:01-Sep-1844Address:County Jail,Parish/District:TRINITY WITHOUTGender:
CountyCo. Waterford
Denomination:Roman Catholic
Father:William MolownyMother:Judith BolandOccupation:
Sponsor 1 /
Informant 1:James Maher Sponsor 2 /
Informant 2:Johanna Stafford
Not sure how you narrow it down but father's & / or mother's name used for William's children could be a clue.
Also (I'm no Waterford expert) Clonmel may be more Waterford than Trinity Without?
Interesting address for the last one - a tough start to life so joining the army at 14 may have been more likely for him?
Col