Genie, see thread 63785, which has a lot of discussion.

Summarising, the oldest dated is "Lady in Love," 1889, found by John Garst- see his posts on this song. The next is "Bright Mohawk Valley," by Kerrigan, 1896. John Garst did a lot of work to find verification of these early versions.
These are the only reliable dates found.

A pencil copy of "Red River Valley" found in Kansas archives has dates 1879 and 188- penciled in, but nothing has been found to verify it.

Edist Fowke seems to have copied her data from an entry in Spaeth and added speculation. Nothing has been found to support her assertions. Both Garst and myself tried without success to find support for her statement.

Canadians say the Red River Valley is the Red River of the North, partly in Canada.
Western Americans say that it is the Red River that for part of its length separates Texas and Oklahoma; its source is in New Mexico where it is a good trout stream in its upper reaches. This river was well-settled from about 1840 on, earlier than the Canadian Red River, but this settles nothing.

As noted in the thread mentioned, "cowboy" versions start with Sprague and Jules Verne, in the 1920s.

Red River Valley