By process of elimination Annie's father is EDWARD
There are 2 Ann Harkin's in Donegal - born 1869 and 1870 with father Edward _ the one born 1870 was baptised in Carndonagh RC Church
familysearch has
Ann Harkin b. 04 Oct 1869 in Burnerana, Donegal
Father's Name: Edward Harkin
Mother's Name: Catherine Mcaleney
using Catherine as the mother's name in I get a hit for both Anns. On this site
http://www.clonmany.com/genealogy/ I found the spelling McAleny and got a match for Annie b.1869
baptism in Buncrana CP
as well as Ann b.1870 also
Nancy Harkin b.29 Jun 1870 in 136, CARNDONAGH, Donegal, Ireland
Father's Name: Edward Harkin
Mother's Name: Cathrine Doherty
Edward and Catherine nee Doherty have other children listed in familysearch
William Harkin b. 18 Mar 1874
Catherine Harkin b. 03 Jun 1872
Biddy b.18 Aug 1868
Fancis Harkin b.13 Jul 1866
James Harkin b.01 Aug 1864
Denis Harkin b. 01 Jan 1876
familysearch has the marriage record of Edward and Catherine nee Doherty in Inishowen 1868
Volume Number: 2
Page Number: 211
The only information I can find for Ann b.1870 is in familysearch
Name: Anne Harkin b.Inishowen 1870
Volume Number: 12
Page Number: 141