"Then I Wasn't Alone" mentions only 2 songs:
  - Pretty Saro - p. 47
  - My Blue-Eyed Boy - p. 47

This isn't really a chapter so-to-speak, but a half-page vignette, but still mentions two songs. Both are just mentioned in passing.

Pretty Saro is an extremely well-known song and has been researched heavily here and elsewhere: Fresno State and Mainly Norfolk both have excellent pages on it.

The second song John calls "The Ring That Has No End." This is a floating verse found in several songs. The Riddle Song usually includes a verse about an un-ending ring, but I find it more likely Wellman was referring to a song of the family of songs based around Blue Eyed Boy due to the fact that John plays it after finding a young boy to play guitar with him; versions of the song go: "It's hard to find a constant friend, / But when you find one good and true, Don't never change 'em for the new. Additionally, the song opens with that line instead of having it as the third verse. You can read more about the family of songs related to Blue Eyed Boy here and here.