I find these marriages on ancestry and since some oare in Washington,Grainger co. which was adjecent to Greene co then is probably this family. There are more and I would gladly look them up and just a bit of information is that some Sarah used Sally. Maybe some of these are yours and you can check these marriages for clues.

Marriages before 1825

Morgan, Thomas Willet, Sally 18 May 1804 Tennessee
Grainger County

Gray, John Morgan, Sally 23 Jun 1804 Tennessee
Grainger County

Follet, Rachael D Morgan, Thomas 18 Nov 1820 Tennessee
Greene County

Morgan, Sally Prather, Isaac 28 Apr 1806 Tennessee
Greene County

Moore, Claibourne Morgan, Sally 17 Apr 1823 Tennessee
Washington County

Carder, David Morgan, Susannah 07 Jun 1823 Tennessee
Washington County