I'm saddened to learn of his passing.
I will always remember him in various Carol Burnette Show skits trying (often, unsuccessfully) to hold composure. That in and of itself would crack me up.
On a recent PBS doc, Pioneers of Television, they said he truly had difficulty holding composure; it wasn't an act. Moreover, Burnette, Conway, and the show's writers would purposely design skits that would "tickle" him.