Mary Jane is one of the two great-greats for Michael who has no known parents. This is partly her fault for marrying prior to the 1850 U.S. census where she first appears with her husband rather than her parents at the delicate age of 20 born in Illinois [1850 U.S. Federal Census for Dade County, Missouri, District No. 25]. She is there with her husband George Carmon and part of his father's family [Joshua and Susannah (Bailey) Carman]. By 1860, this couple had moved to Collin County, Texas, Precinct No. 3 and Mary is listed as age 30, birthplace unknown. [1860 U.S. Federal Census for Collin County, Texas, Page 97]. This family falls out of the 1870 census, or I can't locate them. Their youngest son, born in 1869, claims that he was born in Indian Territory, i.e. Oklahoma. Perhaps the family was living there and there is no census for the "Indian Territory." In 1880, they are back in Texas this time in Grayson County, she age 50, born in Illinois, with a father born in North Carolina and a mother born in Tennessee. [1880 U.S. Census Texas, E.D. 13, Page 22] And that's all the records it seems she generated that I have found to date.
Her husband died in Oklahoma on 18 November 1897. This is from his gravestone record at Falls Cemetery, Cleveland County, Oklahoma. He is buried with his son, Michael's great-grandfather, but his wife is not there. She is not living with that son in the 1900 census.
So, we have no vital records for her at all. She married probably in 1849 or early 1850 either in Dade County, Missouri, or somewhere close by. It is there I would start. We know her maiden name from the death records of two of her children. There are about 15-20 men named Cox living in Missouri, born in North Carolina in the 1850 census who could be potential fathers.
This is an easily solvable problem if one could only do a broad search across geographical areas. But then, of course, if it were that easy, it wouldn't be genealogy.