The John Hopkins Lester S. Levy Collection has sheet music for "Father's a Drunkard and Mother Is Dead", dated 1866. It is clearly related to the "Drunkard's Lone Child" songs, if not the original source. Words are credited to "Stella, of Washington", with music by Mrs. E.A. Parkhurst. I believe that the text and a MIDI can be found at pdmusic.org.