In 1880, Moses and Mary J. Peters were married with one child.
What about Janie's maiden name? It is probable that they married between 1870-1879. Both the death certificate and marriage record are good sources for the 'maiden name'. In addition, any death record of a child could give the maiden name of the mother. Lacking the actual record, I will look for a Marriage record between Moses Peters and Mary/Jane/Jennie --- .

Found.
A Jennie SMITH married Moses Peters in 1877 [Mobile marriages online] ².

I could now focus on the paternal line (Peters) or the maternal line (Smith). I decided to continue with the SMITH line and find Jennie SMITH in 1870. Since she married in 1877, Jennie may be enumerated with her parent(s) in 1870. [A search of the marriage records found no other marriage for Jennie Smith in Mobile County.]

1870 Census, Mobile, AL ³
Russel, John 50 M b works on RR - S.C.
Russel, Mary 52 F B KHouse MD
Smith, Ellen 30 F B at home 250 -- [MD]
--, Mary J. 12 F B at school

Note: This "Mary J." MAY be the one I'm looking for, but with a name like Smith, I need more evidence. Still, she is the only "Mary J. Smith" indexed in Mobile's 1870 Census. IF this is Mary J. Smith Peters, was Ellen Smith her mother? Was Mary Russel her grandmother?

In 1910, Mary J. gave her parents' birthplace as 'Maryland', however other census records showed AL and MS. Since Mary was still alive in 1930, a death record could have the names of her parents. [If this were my family research, I would have ordered a death record for both Mary J. Peters AND Lorna before now.]

Other records could be searched for post Civil war records on the Peters or Smith families.
(1) Voters registrations
(2) City directories
(3) Freedmens Bureau Records [birth, death, letters, contracts, etc.]
(4) Cemetery Records [birth/death dates]
(5) Death Records
(6) Plantation / Farm labor contracts

Sources:
(1) "The American Missionary Association and the Promise of a Multicultural America: 1839-1954." LOUISiana Digital Library Collections Online. Amistad Research Center. [16 Jan 2006].

(2) Index to Marriage Records [online]. Marriage License Division. Mobile County Probate Court. [16 Jan. 2006].

(3) Ancestry.com. 1870 United States Federal Census. [database on-line] Provo, UT: MyFamily.com, Inc., 2003-. Indexed by Ancestry.com from microfilmed schedules of the 1870 U.S. Federal Decennial Census. National Archives and Records Administration. Washington, D.C