Do you have the county and or city in England where she was born? Here are some possibilities:
Eliza Anne Rayner
England Births and Christenings, 1538-1975
christening: 7 February 1866 Thornhill, York, England
residence: Thornhill, York, England
father: Thomas Rayner
mother: Mary Rayner
Eliza Rayner
England Births and Christenings, 1538-1975
christening: 30 December 1866 East Dereham, Norfolk, England
residence: East Dereham, Norfolk, England
father: George Rayner
mother: Harriett
Eliza Ann Rayner
England Births and Christenings, 1538-1975
christening: 1867 MELDRETH, CAMBRIDGE, ENGLAND
residence: Meldreth, Cambridgeshire, England
father: Walter Rayner
mother: Ann
Mary Eliza Rayner
England Births and Christenings, 1538-1975
christening: 12 August 1867 Primitive Methodist, Ely, Cambridge, England
residence: Ely, Cambridge, England
father: Smith Rayner
mother: Mary Rayner
Eliza Rayner
England Births and Christenings, 1538-1975
birth: 3 June 1855
christening: 11 September 1865 SAINT DAVID, BIRMINGHAM, WARWICK, ENGLAND
father: Thomas Rayner
mother: Emma
Mary Eliza Rayner
England Births and Christenings, 1538-1975
christening: 12 August 1867 Primitive Methodist, Ely, Cambridge, England
father: Smith Rayner
mother: Mary Rayner
Eliza Ann Rayner
England Births and Christenings, 1538-1975
christening: 4 August 1867 MELDRETH, CAMBRIDGE, ENGLAND
father: Walter Rayner
mother: Ann
Eliza Rayner
Daughter
United States Census, 1880
birth: 1865 England
residence: 1880 Philadelphia, Philadelphia, Pennsylvania, United States
father: James Rayner
mother: Sarah Rayner
other: Armitage Rayner
Eliza Rayner
England, Norfolk Bishop's Transcripts, 1685-1941
christening: 30 December 1866 East Dereham, Norfolk, England
father: George Rayner
mother: Harriet Rayner