Just to confirm that the parents of James Farrell were Thomas Farrell and Marie Carthy? I searched on the subscription site Roots Ireland and the free site www.irishgenealogy.ie and did not find a baptismal record for James Farrell. I also did not find a record for Elizabeth Bray with father Edward.
I did locate the civil marriage record for James and Elizabeth which shows their fathers names and the birth record for Mary Farrell.
Mary Farrell 1883 see fourth record https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_return...