I think Jeremiah is James' father because James' daughter is living with him shortly after James' death.
Sources
"United States Census, 1870," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MZ55-M71 : accessed 10 December 2015), Jeremiah Hannigan in household of Michael Mccarty, Pennsylvania, United States; citing p. 244, family 1923, NARA microfilm publication M593 (Washington D.C.: National Archives and Records Administration, n.d.); FHL microfilm 552,904.
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