It's in these lines:
Dinner in the diner, nothing could be finerThey're talking about the food available on the train, but it seems to imply that the passengers eat ham and eggs (which I'm fairly certain are breakfast foods) for dinner.
Than to have your ham and eggs in Carolina
It might just be two separate meal times that are squished together because of the phrasing, but - in that case - I think a word or two could have been changed or added to prevent any misunderstanding.