Okay, to sum up: You are looking for descendants of Jacob Michael King and Martha Powell who lived in Rankin County, Mississippi Leake County, Mississippi Madison County, Mississippi
You know Jacob Michael King and his wife Martha died in Sharon, Madison County, Mississippi. They are buried in Good Hope, Leake County, Mississippi.
You say, "They have one son buried there." CAN YOU ADD HIS NAME? Date of birth? Wife's name? Children's name?
You say another son, William Randolph King, is buried in Straight Bayou, Richey, Sharkey County, Mississippi. CAN YOU ADD HIS WIFE'S NAME? CHILDREN'S NAMES?
I believe you are referring to this man: William Randolph King Born 21 April 1878 Died 14 December 1935 buried Straight Bayou Cemetery, Richey, Sharkey County, Mississippi, per Find a Grave
You say you know of living descendants of him, but cannot locate in www.whitepages.com
It's good not to talk about living people in a genealogy forum, and you didn't. However, you are allowed to list the names of the children of a man who was born in 1878.
There are so many people of similar names and ages in the areas you mention, that I honestly cannot DEFINITELY identify your family without considerably more research - which seems silly, since you already know their names.
Hope you don't mind me asking you for still more information. I do think it will help if you add more.