Maxwell House worked with Ray from 1981 to 1985. The jingle was composed (uh-uhm) by Joseph Brooks (source: New York Times, August 29, 1982).
In this interview, Ray speaks about the reason why his name wasn't mentioned when the campaign ran.
(Commercial #1 on this reel):
(Last commercial on this reel):
Ray also contributed to a Maxwell House radio commercial (or was it with the same jingle?) in 1982. And this aired in 1985.