Is there a company that makes automatic transmissions for the Harley Davidson motorcycle?

No, BUT , There are several Automatic clutch systems available . one would be able to shift , or actually need to shift through the gears manually , with the exception of at idle and when the throttle is let off. the clutch automatically disengages. will not work on bikes with a kick start only starting system . electric start only. there are also shift drums available that changes the position of neutral . so all shifting becomes all one direction instead of on down and 3 ,4 , or 5 up . makes for simple shifting distraction riding for beginners and people with physical limitations .