Well, it looks like the earliest printed version indexed is in an 1859 book called Songs of the Florences. It's at the Washington State University library in Pullman - anybody know how to get documents from them?

In the meantime, I found a song in Punch (December 31, 1881) that's sung to this tune:

VICE VERSA; or, LINES ON A PULLMAN CAR
Air: My Johnny Was a Shoemaker!

Oh, riding on a Pullman Car!
To Brighton by the sea
In an hour and a qua-ar-tar!
Is the thing that just suits me.
There's a drawing-room, parlour, smoking-room, and bar
For Mocha and the best Bohea-ea-ea!
Oh, don't I like a Pullman Car!
Lighted by electricitee.