I have horribly vague memories of this, but lasting ones. I played it on a Radio Shack Tandy Color Computer 2 (maybe the CoCo 3, but I think it was the CoCo 2). It was a point-and-click adventure which included traveling back and forth in time. I am 90% certain that it was set in a museum. It was fairly monochrome, typical for the time. I remember traveling back to a medieval dungeon and also a situation where, to get the diamond, you had to take a lump of coal back in time, put it in a hydraulic press, then go forward in time until it became a diamond. I'm pretty sure one of the game screens had a vintage car on display.
It being on the CoCo 2 puts its publication somewhere between 1983 and 1986.