How to ground a vintage device that was powered without a ground?
Nothing. AC doesn't need ground to function if it has neutral line. You can just put a 3 pin plug and not connect anything to ground pin if you must use a 3 pin plug. 

If you want to implement the ground yourself for say additional safety, post pictures of the insides of the charger (In fact post pictures of the insides in any case! We may identify some component that may have failed over time with them). Most such devices I've seen just have the ground wire connected to the case of the device.

If you find electrolytic capacitors somewhere inside, do change them! They tend to wear out with time.