I thought I was working on this song just the other day, but I can't find where I did whatever I did. These ethnofolkmusicologists at the Traditional Ballad Index don't have anything on the song, but there is a Wikipedia article that says this:

"Down by the Station" is a popular song written by Lee Ricks and Slim Gaillard in 1948, and most famously recorded by Tommy Dorsey. The song remains popular today as a children's music standard. The opening lines of the song are: Down by the station, early in the morning, see the little pufferbellies all in a row. The song itself is much older than 1948; it has been seen in a 1931 Recreation magazine.
Whether deliberately copied or not, the tune is very closely related to the chorus of the French/Canadian folk song "Alouette".
The Four Preps recorded a version of the song in 1959, featuring an entirely different set of lyrics by group members Bruce Belland and Glen Larson.

My heart sank when I saw it was written by Lee Ricks and Slim Gaillard in 1948, the year of my birth. I was very glad to see that it had been seen in a 1931 magazine.
Maybe I came across "Down By the Station" a couple weeks ago, when we were working on I'm a Little Teapot, another song that we can trace only back to the 1930s. It just doesn't seem right that these two songs are so recent.
Either that, or if they're NOT recent, then I'm really old...

-Joe-