Only thing I can find is an 1850 Federal Census Record
If you move forward 20 years you have the 1870 Census
Anna on the 1870 Census appears to be Ann on the 1850 Census
I looked back at the 1820 Federal Census for North Carolina
Only 2 Male names that start with M for Griffin Surname appear to be Moses and Matthew however they could have moved out of North Carolina by 1820
Ann Griffin
Born: 4 Aug 1830
Died: 22 Feb 1924
See: Find A Grave Memorial 16882445
George Griffin
Born: 2 Jan 1838
Died: 27 Nov 1900
See: Find A Grave Memorial 13355123
I cannot guarantee the information posted here is for the same family although a possibility.