Here's what I know:
Martha T. Ryerse born in Canada, Daughter of Martha and Adam W. or Aurthur W. Ryerse.
Found in the following census:

1860, Cordova, Rock Island, Illinois
Adam W., head, age 36, Born in canada
Martha, wife, 32, New York??
Martha, daughter, (this is the one I'm asking about) 7, Canada
Mary, 2, Born in Illinois

1870 Cordova, Rock Island, Illinois
Riorsy, Mary, age 43, Keeping house, Born in New York
Martha, 17, Canada
Lina, 12, This census says that she's a male!, Illinois

1880, Cordova, Rock Island, Illinois
Williams Daniel P., age 45, Penn
Martha T. (wife), 28, self born in canada, mother and father both from Canada
Ora P. (son), 3, Illinois
Ryerse, Linna J. age 22, Sister In Law, Illinois, Canada, Canada