12-stringer is of course correct about the song's writers. I was looking for chords and copied the lyrics from a sight dedicated to Hawkshaw Hawkins. Their credits are bogus.

TWO LITTLE BOYS
Lyrics by Edward Madden
Music by Theodore F. Morse

Madden is credited with "Moonlight Bay" and "By The Light Of The Silvery Moon".

Here is another take on Madden's career:

"Despite his successes, some of Madden's output looms a lot closer to that of his song-poem customers than to his legit-music colleagues. A song he wrote in 1907 bears the intriguingly song-poemish title, "Way Down In Colon Town," and in his lyric to "My Cousin Caruso" we find the immortal couplet, "His voice so dreamy / Like da peaches an' creamy." Caruso, upon hearing the song, is said to have belched."