I haven't read any of the books I'm suggesting but I used an online reader’s adviser used in many libraries called, "NoveList". Be sure to see if your library has this wonderful resource. You can actually put in a plot and it will list the books with that plot. Here are some results:
Freedom Run by Rina Keaton (1994 Holloway House) might be good. I couldn't find a review but the subject headings included New Orleans, 19th c, and African-American women.
Tane River by Lalita Tademy According to the Booklist review: "Tademy halted a career as a high-powered technology executive to research her family’s history. Her findings--four generations of strong-willed black women who survived slavery and racial injustices, maintained strong family ties, and left a legacy of faith and accomplishment--are transformed here into a powerful historical novel."
Abraham's Well by Sharon Ewell Foster is a book in which "Armentia, an aged black Cherokee woman, remembers her youth, her family, and their struggle to hold on to their dreams". A book review from Library Journal says, " Focusing on the history of African Americans as well as Native Americans who were forced to walk the Trail of Tears in the 1800s (see also Al and JoAnna Lacy's Bright Are the Stars, right), Christy Award winner Foster (Passing by Samaria) has written a sensitive portrayal of one woman's struggles and hopes. --Tamara Butler (Reviewed November 1, 2006) (Library Journal, vol 131, issue 18, p62)". So, this is more of about about the journey to Oklahoma.
I'm sorry I don't have more results but I hope this helps. Good luck!