If you look on rootsweb, there are some trees for Duriman Buxton. They list Synthia Coker's parents as John and Rosaline Snoddy Coker. Here is the 1870 census. I wonder if the family in the dwelling before Mrs. John Cocker is Rosline's mother? Ancestry has Sintha indexed as Lintha Cocker. The actual page reads Sintha.

Source Citation: Year: 1870; Census Place: Subdivision 6, Avoyelles, Louisiana; Roll: M593_506; Page: 339; Image: 50.
29 Jun 1870
400/443
SNODDY, Andrew Ms., 52, F, W, Keeping house, 200/100, LA
-----Celina, 25, F, W, At home, LA
-----Cornelia, 21, F, W, At home, LA
-----St. John, 17, M, W, At home, LA
-----Thomas, 14, M, W, At home, LA
-----Catherine, 12, F, W, At home, LA
-----Louisiana, 10, F, W, At home, LA

401/444
COCKER, J. Ms., 31, F, W, Keeping house, LA
-----Mary, 14, F, W, At home, LA
-----James, 14, M, W, At home, LA
-----Wm, 10, M, W, At home, LA
-----Sintha, 9, F, W, At home, LA
-----John, 6, F(M), W, At home, LA

**************
Source Citation: Year: 1860; Census Place: Not Stated, Avoyelles, Louisiana; Roll: M653_407; Page: 0; Image: 415.
10 Nov 1860
842/842
John COCKER, 29, M, Farm laborer, -/100, LA
Roseline, 21, F, LA
Mary, 6, F, LA
James, 4, M, LA
Bryent, 1, M, LA