Center Controller reported an aircraft lost its autopilot and instrumentation requiring a diversion to a nearby airport.

Narrative

Aircraft X was enroute from ZZZ to ZZZ1. Over LSF he began to turn 20-30 degrees right of course and climb 300-400 feet. I asked the pilot if everything was alright and he responded he lost his autopilot. I advised him of the weather ahead and to keep me informed if he needed any assistance. 2 Minutes later; I lost his Altitude readout. I broadcast to the pilot to I lost his Altitude and to reset his transponder. I received no reply. The aircraft turns abruptly and circles LSF airport. At this time; my side begins to coordinate with Atlanta [TRACON] and I relay the information to my supervisor. I am broadcasting to the aircraft; attempting to have him respond via ident; trying on guard. I receive no communication with the aircraft. The aircraft makes a circle around LSF and begins to trek due west. I continuously broadcast to him to try and raise him; and inform him of potential airports he could land that. I broadcast the MIA (Minimum IFR Altitude) for the area. My supervisor informs me that they received a message that he was talking to MGM Approach he had lost all instrument function and had very basic power and was going to divert to MGM. I continue to relay all possible airports enroute to MGM and the MIA until the aircraft landed safely at MGM.