Mark, although not the names one typically associates with Arkansas (Hindman, Cleburne, etc), in his book More Generals in Gray, [LSU Press, c. 1995,] Bruce Allardice enumerates 10 generals associated with Arkansas as their "State of Service," although none were born in Arkansas:

Thomas H. Bradley (member of Arkansas Secession Convention)
Napoleon Bonaparte Burrow (Allardice states: "Burrow's rank of general in the Arkansas state army qualifies him to be considered a Confederate general.")
Archibald S. Dobbins (had moved to Arkansas by 1850)
Edward W. Gantt (raised the 12th Ark Infantry)
Thomas Hamilton McCray (originally enlisted in the 5th Ark Inf)
Samuel Preston Moore (surgeon general of the Confederacy, practicing medicine at Little Rock in 1861)
John Edward Murray (buried at Mount Holly Cemetery at Little Rock)
Nicholas Bartlett Pearce (appointed brigadier by Ark Secession Convention in May 1861)
James Spencer Rains (a farmer from Newton and Jasper counties, Ark militia/also Missouri militia)
James Yell (elected as major general of the "Army of Arkansas" by the secession convention)

Allardice references an article entitled "Confederate Generals from Arkansas," by Jno. P. Morrow Jr., that appeared in the Arkansas Historical Quarterly, XXI (1962), 231-46, where more information may be located.