Sweet Potatoes

This Creole folk song from the Louisiana Bayou makes for a beautiful partner song when paired with Mango Walk.
Sources: Seeger, Pete.  Fireside Book of Fun and Game Songs.
Silver-Burdett Music Text

Phoebe

I love this song paired with a partner song composed by Denise Bacon.  The soaring octave jump in the partner song would be great for those vocalists who love to sing high and show off a beautiful voice.  It would also sound great played on instruments.
Source: Bacon, Denise.  46 Two-Part American Folk Songs

My Paddle

This song sounds lovely when it's paired with a partner song, as Denise Bacon does, or sung in a round.  It's also great for presenting the syncopated eighth-quarter-eighth (or "syncopa") rhythm.
Source: Bacon, Denise.  46 Two-Part American Songs

Mango Walk

Mango Walk is a Jamaican Calypso tune that can be sung as a partner song with Sweet Potatoes.
Source: Silver-Burdett Music Text

Bye Bye Baby

Denise Bacon has written a lovely partner song to perform with this Appalachian lullaby.
Source: Ed. Erdei, Peter. 150 American Folk Songs to Sing, Read, and Play p. 6
Two-Part Version: Bacon, Denise.  46 Two-Part American Songs