Here is some more info from Coweta County Chronicles which appears to come from an old bible:
PHILLIPS FAMILY RECORD.
William D. Phillips, born Janury 20, 1768, married August 26, 1796, Mary Spratlin, born April 28, 1807.
(a) James S. Phillips, born November 17, 1799, married Elcy Phillips May 26, 1824; children:
1. Amelia Ann Phillips, born April 24, 1825.
2. Tillitha Jane Phillips, born November 28, 1826.
3. Mary H. Phillips, born March 22, 1829.
4. Caroline Elizabeth Phillips, born January 21, 1831.
5. James Henry Phillips, born February 5, 1832.
6. Elijah William Phillips, born February 24, 1833.
7. Elcy Phillips, born Janury 17, 1837.
8. Tillitha W. Phillips, born November 15, 1838.
9. John Darwin Phillips, born March, 1841.
10. Frances Amanda Phillips, June 22, 1843.
11. Louisa Phillips, born August 13, 1845.
12. Arabella Phillips, born November 2, 1847.
13. Joel Haden Phillips, born November 2, 1848.
Source: Coweta County Chronicles, by Mary G. Jones and Lily Reynolds, printed by The Stein Printing Company, Atlanta, GA., 1928; Pgs. 797-798
The biggest discrepancy seems to be Caroline Elizabeth's date of birth.The bible record said she was born Jan 21 1831.You say the tombstone for your Caroline Elizabeth Phillips gives Jan 1 1836 as her birth date.Of course, it is possible that during her life she lied about her birth date to make it appear she was younger than she actually was.Women have been known to do that.Another problem is she does not appear to have named any of her children after her father or mother, which was unusual back in those days.I don't know when or where James S. Phillips died, so I don't know if he left a will.It would also behoove you to look for any will left by Elcy/Alcy.
Phillips DNA Project