look here
https://www.mcmaster.com/#light-duty-gearmotors/=h0nyjw at the ac motors, not controllable, but you have a choice of speeds scroll down to the Synchronous AC Gearmotors or on down to the DC motors which would be controllable by varying the DC voltage.
Your choice may depend on how much room you have behind the painting and how you can mount the painting, but if it's balanced, torque may be minimal and you would need to worry about is the weight of the setup and the forces of gravity.