Hi Sandra I have a great-grandaunt named Amanda E. FINE. I haven't found out if she was born in Washington County, Tennessee, but her father was. Her father is Abraham FINE and her mother is Jane CANNON. The only thing is the dates don't seem to fit the Amanda you mentioned. Amanda E. FINE was born 1859 and her father Abraham FINE was born about 1822. She married a man whose surname is LEONARD.
Are you sure you have her birth year correct? If so, maybe she is still related to this FINE family. I have another Amanda FINE in my line. Her name is Amanda J. FINE, born 1891. She is Amanda E. FINE's niece and the daughter of Allen Buchanon FINE. I don't have any other information on her.