I believe I have identified the song that several Mudcatters have quoted above:

RAIN AND THE RIVER
Words by J. Will Callahan (1874-1946); music by Oscar J. Fox (1879-1961); copyright 1936.
Sheet music published by: C.C. Birchard & Company, Boston.
First line of verse: River looks black with the shadows on it
First line of chorus: I loves the rain, and I loves the river
Sheet music held by (and this information provided by): Baylor University – Arts and Special Collections Research Center

Unfortunately, the sheet music is not viewable online because the song is still under copyright.

You might be able to find the sheet music in a library near you by following this link to WorldCat.org.

On YouTube, I found a recording by the 1983 Calhoun High School Concert Choir (of Merrick, NY) but some of the words are incomprehensible to me; you might have better success at transcribing it if you are aided by memory. I think I get the gist of it, though – and I find it rather incredible that a person would be so complacent about seeing his cabin and farm wiped out by a flood because he “loves the rain and … the river.” Are there racist assumptions built into this song? (The song seems to be written in dialect, so I assume the narrator is supposed to be black. Funny how we don’t question things if we grow up with them.)