I am not sure if Martin J. Kington had a son by the name of Martin either.

Wm. B. Kington (William?)
Malissa Kington
Louis Kington
John R. Kington are the children listed in the 1860 Cherokee Co. AL census, but I know they had Mary Lucinda Kington also. I show Broomtown area of birth's for most if not all. I lost them after that, but appears Louis & Malissa buried in Broomtown at Church of Christ. So not sure that Martin and Martha left area. Unless they left later.