Debra, I wish I could help you out. I looked for Clemency Barnhill.. in fact I looked for any Barnhill in my books but no luck. From the census info we can assume that she married about 1817 to a Mr. Jennings? My suggestion would be to write to the Scott Co. courthouse to see if they have any record of a marriage for them. Scott Co. 101 E. Main Georgetown, Ky 40324 Include a SASE so they can respond easily.
My other suggestions would be to see if there is any record of the births of the Jennings children. Sometimes it includes names of both parents. Another option would be to see if there is a death record for any of the Jennings children. If they died late enough(after 1911) there could be a mention of the parents. These are both long shots I know. Another long shot would be to look for a civil war pension claim for one of the sons. Sometimes it will contain the names of the parents.
Have you tried looking at the 1820-1840 census for any Jennings in Scott co. that might fit? If one of them does you could ask Scott co. if they have a will and/or probate for him. It's possible it would name dependants.