I can't tell you this with absolute certainty because all I know is where the current activity is for natural gas prospecting in the Fayetteville Shale. This is a hot new area that lots of smaller oil companies are getting into, and at least one major, Shell, has also started leasing. The company that is the most active in the area is Southwestern Energy Company in Houston who is planning to spend $338 million this year exploring and drilling in the Fayetteville Shale. They have planned 175-200 new wells.
The counties where the major activity is taking place suggests this is where the oil company geologists believe the Fayetteville Shale is located. The counties I know of are:
Franklin, Johnson, Pope, Yell, Conway, Van Buren, Faulkner, and Cleburne.
Looking at the map, I believe that at least parts of Logan County and Sebastian County are probably included. The actual area might be larger because the petroleum companies are only interested in finding the shale where it is the thickest. This shale contains a lot of natural gas. The top of the shale varies between 1500 to 6500 feet deep, so it is shallow and easy to drill.
All of the maps I know of are proprietary, and very expensive. Geomap has a vague outline of the map they sell at: http://www.geomap.com/item12.html
To find out what counties are involved I looked through a lot of trade industry publications, most of which are also fee based subscriptions. One free website where you can look for news is Rigzone. The link is below. The stratigraphic column is at: http://www.state.ar.us/agc/stratigr.htm
You can buy a map from the state of Arkansas here
http://www.state.ar.us/agc/agc.htm