I have almost NO info to go on. It popped into my head while I got up to go pee about 1/2 hour ago. It MAY have been a Dr. Demento song; I’m not sure. It’s got a piano opening, and it sounds ragtime. The opening is close to - but not quite - Tom Lehrer’s Vatican Rag. Maybe with I Will Survive mixed in. The lyrics start out with something about (I believe) “ever since I was a little bitty kid, my momma [or mother, or some other term]…” something. It may reference something being placed above his crib, like a mobile or something.
As “My Ding-a-Ling” was recorded before a live audience with only Chuck Berry’s guitar as musical accompaniment, it wouldn’t appear to match the OP’s description (“It’s got a piano opening, and it sounds ragtime. The opening is close to - but not quite - Tom Lehrer’s Vatican Rag. Maybe with I Will Survive mixed in”) very well.