The 1870, 1880 and 1900 censuses list her birthplace as Massachusetts. Her death records and her son's census records list her state of birth as New York.
Taken from Portrait and Biographical Album of Fond Du Lac County, Wisconsin: Containing Full Page Portraits and Biographical Sketches of Prominent and Representative Citizens of the County, 1889. In Binghamton, Broome Co., N. Y., Mr. Rogers was united in marriage with Miss Arabella Barnum daughter of Dr. Forward Barnum of Berkshire County, Mass, and a cousin of P. T. Barnum, the eminent showman. (Note: they were fourth cousins once removed).
She is Find A Grave memorial #98753366 and is linked to her parents and some siblings.