Hi Liz and Sancti,
I have just done a search on IGI for children of Bernard Finegan (or similar) to a Mary. Backs up Bernard in Barnshill being widow of a Mary Feely, so definitely not your one.
On LDS Family Search site, checking family of a Bernard Fin*egan marrying a mary Marrow or similar
Parents Bernard Finegan and Mary Marron: -
Rose Finegan 06 Jan 1865 0555 Raferagh, Monaghan
Anne Finegan 05 Aug 1867 0459 Raferagh, Monaghan
Frances Finegan 19 Jul 1870 Monaghan Ireland
Bernard Finegan 19 Jan 1876 Monaghan Ireland (Manon was surname but lumped with Marron)
Parents Bernard Finnigan and Mary Martin
Patrick Finnigan 03 Apr 1863 Clyde, Glasgow
Parents Bernard Finegan and Mary Feely: -
Bernard Finnegan 08 Aug 1874 Anderston, Glasgow
Frances Finnigan 08 Apr 1869 Middle or New Parish, Greenock
Patrick Finagan 12 May 1871 Anderston, Glasgow
Parents Bernard Finegan and Mary Coyle: -
Bernard Finigan 29 May 1866 0238 Scrabby District, Cavan, Ireland
Parents Bernard Finegan and Mary Conery (Cooney, Canney etc): -
Margaret Finegan 03 Feb 1866 Armagh, Ireland
Mary Anne Finegan 26 Aug 1867 Armagh Ireland
Patrick Finegan 28 Feb 1869 Armagh, Ireland
Susan Finegan 03 Nov 1870 Armagh Ireland
Lucy Bridget Finegan 31 Dec 1873 Mount Norris, Armagh, Ireland
Bernard Finegan 16 Jun 1879 Ballintemple, Armagh, Ireland
I think our Alice could be born to first Bernard, husband of Mary Marron, but not much room to fit a brth in between Rose and Anne. Have a look at this and see what you think.
Tom