A lot of the Southern streaks depend on whether you count the appointed offices in the Reconstruction era. In terms of present-day streaks, I imagine any others that meet or exceed the MS AG's streak have already been mentioned.
As of now, the MS AG race will finish with at least 146 years of Democratic control, but a more prominent statewide office - Governor of Georgia - was held by Democrats for 150 years (at least in terms of elected terms; 1853-2003).
There are other less clear examples as well. For GA's Attorney General, it's hard to say (given that there were no AGs with formally declared political affiliations from 1834-1868), but this office was held by Democrats from 1872 to 2011 (139 years), with the last publicly identified (non-Reconstruction) AG with partisan affiliation being a Democrat, from 1831-1834. It's not a stretch to assume that a continuous line of Democrats from 1831-2011 (180 years) held this particular office, though not all explicitly as "Democrats".
This thread is several years old but also has some data-points in it as well.
