John B. Green (Greene?) born ca1808 in TN

I am having no luck in locating parents and other ancestors of my gggrandfather, John B. Green(e), who shows up in the Franklin County, Alabama 1850 census and is recorded there along with his wife, Elizabeth, and their first two children as having been born in Tennessee. At that time he was recorded as being 42 years old, and his wife 36. They subsequently moved to Pontotoc County, Mississippi. I have the documentation for my line starting with him, but have had no luck at all in going back in time from 1850. Does anyone have anything to help me in that search? Thank you in advance.