I've checked both the Prairie Home Companion site and Allmusic.com, and this is the song that Jearlyn Steele sang, and that Los Lobos recorded.

Lyrics and chords copied from http://www.guitaretab.com/l/los-lobos/10747.html

DOWN ON THE RIVERBED
David Hidalgo and Louie Pérez (members of Los Lobos)

   A
  Down on the riverbed,
    E
  Down on the riverbed,
    A
  Down on the riverbed,
      C             G        A   C  G  A
  I asked my lover for her hand.

A red-tailed hawk circled overhead. (3x)
"The church on the hill" was what she said.

A monster cloud like a big black hen (3x)
As she drew houses in the sand.

REPEAT FIRST VERSE

Then I heard a train whistle blow, (3x)
And I knew it was time to go.

REPEAT FIRST VERSE

I asked my lover for her hand. (3x)

[Recorded by Los Lobos on "Neighborhood" (1990), "Just Another Band from East L.A.: A Collection" (1993), "My Family" (1995), and "Cancionero: Mas y Mas" (2000). Kate MacKenzie also recorded on her albums "Let Them Talk" (1994), and "House on Fire" (1995).]