perhaps the parents are different..........

Not sure if this discounts this family

daughter Mary Morriarty (as spelt) born 3 Sept 1865 - died 6 June 1931
parents Edward Morriarty and Jane Ferriter. Informant Katherine Morriarty - sister.
burial St Marys Cemetery.
Giles Morriarty on the 1871 census could be Dominick Giley Moriarty born 4 August 1854 to Edward and Jane. Massachusetts Town and Vitla Record.
Sandra