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Below is the likely 1901 and 1911 census records for the Mulligan family. It looks like Mary was born closer to 1884 although I was unable to find a baptismal/birth record in Co. Westmeath. I did find the civil marriage index record and the church record of the marriage in 1876 in Delvin.
First name(s)PeterLast nameMulliganRegistration year1876Registered Quarter/Year1876Registration districtDelvinVolume3Page201 MarriageFinder™Peter Mulligan married one of these people
Anne Smith, Elizabeth Hughes, Bridget Seery, Ellen Fagan
First name(s)PeterLast nameMulliganAddress-Marriage year1876Marriage date20 Feb 1876ParishDelvinAlternative parish namesCastletowndelvin, Crowinstown, Delvin, Crowinstown, Killulagh and Killeagh, Killeagh, KillulaghDioceseMeathSpouse's first name(s)EllenSpouse's last nameFaganSpouse's address-CountyWestmeathCountryIrelandRepositoryNational Library of IrelandNational Library of Ireland linkhttp://registers.nli.ie//registers/vtls000635129#page/1/mode/1upRegisterMarriage