Gee! I always knew it as "The Eyes of Texas."
(OK, back to my cage).

Nothing found earlier than "The Levee Song," 1894, as noted by Joe.
In addition to the printing in Carmina princetonia, sheet music to "The Levee Song" was published by Hinds, Noble and Eldridge, 1900 (note in Scarborough).

Most of the verses sung with it are add-ons, from "Down on the Ohio," "Down Went Maginty," "In the Evening by the Moonlight," "Hear dem Bells," etc. (Noted in no. 234, Work Songs, The Frank C. Brown Collection of North Carolina Folklore, vol. 3).
Neither Newman I. White, American Negro Folk Songs, nor Dorothy Scarborough, On the Trail of Negro Folk-Songs, considered it to be of Negro origin.
Scarborough recorded an add-on verse, from minstrel shows-

Sing me a song of the city,
(Roll dem cotton bales)
Darky ain't half so happy
As when he's out of jail.
Mobile for its oyster shells,
Boston for its beans,
Charleston for its cotton bales,
But for yaller gals- New Orleans!