I have found the 1900 census for her two sons, William H. and Orion E. O'Brien. William listed his mother being born in Long Island and Orion listed her being born in Connecticut. But on the 1870 census for James O'Brien, she listed her birth state as New York and both her parents were born in the state of Connecticut.
1850 - US Federal Census for Janesville, Rock County, Wisconsin (West side of Rock River)
Obrien, James 28 shoemaker $1,100 Wisconsin
Obrien, Eliza 20 WI
Obrien, Edward 8/12 WI
1860 - US Federal Census for Janesville, Rock County, Wisconsin
Obrien, James 41 m farmer $3,000 estate, $570 personal NY
Obrien, Eliza J. 30 f NY
Obrien, Edward J. 10 m WI
Obrien, Wm H. 8 m WI
Obrien, L. C. 5 m WI
Obrien, Alfred 3 m WI
Obrien, Charles C. 1 m WI
Eaton, Minerva 33 f NY
1870 - US Federal Census for Janesville, Rock County, Wisconsin (Roll # M593_1736, Image 7, taken on July 6th, page 181)
743James O'Brien 53 Farmer Ireland
Eliza 40 Home Maker New York
Edward 20 R.R. Brakeman Wisconsin
William H. 18 R.R. Brakeman Wisconsin
Leroy 15 Wisconsin
Alfred 13 Wisconsin
Charles 11 Wisconsin
Orion 9 Wisconsin
Hattie 5 Wisconsin
Mattie E. 3 Wisconsin
1880 - US Federal Census for Janesville, Rock County, Wisconsin (from LDS entry, p 164 D)
James 62 self Farmer Ireland Ireland Ireland
Louisa Jane 50 wife New York Connecticut Connecticut
Orien E. 18 son Wisconsin Ireland Connecticut
Hattie J. 15 daughter Wisconsin Ireland Connecticut
Mattie E. 12 daughter Wisconsin Ireland Connecticut
Cora may 9 daughter Wisconsin Ireland Connecticut
1900 - US Federal Census for Janesville, Rock County, Wisconsin - South Main Street
OBrien, Eliza head Oct 1829 90 w radio 9 children / 7 alive NY CT CT Capitalist owned her own home
OBrien, Cora M daughter Feb 1871 29 S WI Ire NY Machine operator