They need to emulate the West Virginia Democratic Party. All of these statewide offices are competitive if they can run the right candidates. Someone mentioned Walter Maddox in the thread, and he would be a good pick for doing just this. Alabama just needs some time to find its Joe Manchin/JBE/Jim Hunt.
Rigid racial dynamics make it a lot more difficult in Alabama than West Virginia.
However, there is one fairly interesting quirk about Alabama that may or may not matter: the unionisation rate compared to every other Southern state.
The industrialization of the South presents the Democratic Party with a great opportunity. If there can be a concentrated movement to get Southern workers to unionize en mass, then the Democratic Party could create for themselves a brand new voting base. As factories shutter in the Rust Belt, new ones open up in Dixie.
If the national Democratic Party can get serious about expanding union rights and striking down right-to-work laws, they will see their margins in the South improve for all offices. The party really has nothing to lose by doing this.