The two possible names that I come up with for Joseph's wife are Mary A. Hess or Mary A. Kever/Keiver.
When their daughter Elmira/Almira Correll McConnell marries John A. Peters in 1899 Vigo Co., she says her father is Joseph Correll and mother is Mary A. Hess. (Elmira was first married to Benton McConnell.)
When their son Henry Shelby Correll marries in Iowa in 1917 and 1919, both times he says his father is Joseph Correll and Mother is Mary Kever/Keiver.Also, in the 1925 IA census(2nd page) he says his father is Joseph Correll and mother is Mary Kever. (Shelby was first married to Elizabeth (Lizzie) King.)
Because censuses before 1850 only listed the heads of households, and death certificates weren't issued until years after her death, the only shot at tying Mary to a family will be a will or a marriage bond with a relative listed - both are unlikely.