Here are the listings for the 1860 Covington County, Alabama census.
Curington Joseph G. 20 M W GA AL COVINGTON 1860 Rebecca A.24 F W MS AL “ Mary C. 2 F W AL AL “ Albert 6/12 M W AL AL “
Curington Albert 45 M W GA AL “ Louanna 50 F W GA AL “ Marion J. 18 M W GA AL “ William T. 13 M W GA AL “ Louanna U. 9 F W GA AL “ George Ann A 7 F W AL AL “
Curington Dock 27 M W GA AL COVINGTON 1860 Virginia 24 F W GA AL “ Madora 4 F W AL AL “ Lucinda A. 6/12 F W AL AL “
Let's see what else...there is an Upson County, GA marriage record for Albert Cureton to Lovana (or Louana) Pye November 11, 1835. Other Cureton marriage records in Upson are: Cureton, Anna A. Bryant Jernigan 12/19/1841 Cureton, Sarah James H. Jones 5/9/1847
Albert Cureton is listed as head of household in the 1850 Upson Co, GA census. Cureton, Albert 34 MGA Susanna 40GA Joseph G. 11 GA Marion J. 8GA William ?. 4? GA Susanna1GA Elizabeth 62 GA
There are also listings for a James Cureton age 52 & family in the 1850 & 1860 Upson County census (age 55).(His wife's name is Phebe, so I'll go ahead & mention there is a marriage record in Hancock Co., GA for a Cureton, James & Phebe Patterson 12 Aug 1813) & listings for a Hannah, James, & William Cureton in the 1830 Upson Co. census.
I have a couple of questions for you. (1) How did you ascertain that Joseph Green Curington was born in Houston County, Georgia? (2) Do you have any idea how he might have gotten the middle name of Green?
I have been able to trace my line of Curingtons/Curetons to Talbot County, GA, a neighboring (SW) county to Upson. My ggg-grandfather John Cureton (Curington in later Alabama censuses) b. 1814 m. Martha Ann Emerson 1839 in Talbot Co.He appears in the 1840 Talbot Co, GA census next to William & J. Green Cureton.Dickson & James Cureton are also listed in the 1840 Talbot Co., census.Can't connect them to earlier documented lines of Curetons.