IMDb has quite the list of songs included in the movie:

Home in the Meadow to the theme of Greensleves, sung twice: once at the intro by Debbie Reynolds, Karl Malden, Agnes Moorehead and others, and once at the end by Debbie Reynolds, George Peppard, Carolyn Jones and children

Raise a Ruckus performed by Debbie Reynolds, lyrics adapted by Johnny Mercer

A fragment of Wait for the Hoedown, sung by Reynolds again

What Was Your Name in the States? again performed by Debbie

I'm Bound for the Promised Land, with music and lyrics by Ken Darby and Robert Emmett Dolan

Shenandoah sung by Ken Darby

(Fifteen Miles On) the Erie Canal is a traditional song sung by Dave Guard and The Whiskeyhill Singers

Rock of Ages with lyrics by Augustus Montague Toplady, and performed by "all" at the Prescotts' burial

Nine Hundred Miles from Home; lyrics by Ken Darby, sung by "a Chorus"

When Johnny Comes Marching Home sung by Ken Darby

Battle Hymn of the Republic sung by "a chorus"

Come Share My Life, written and sung by Alfred Newman

On The Banks of Sacramento, music by Newman, lyrics by Darby

Overture: I'm Bound for the Promised Land/Shenandoah/Endless Prairie (possibly what Sorcha was referring to?), with music and lyrics by Darby and Robert Emmett Dolan, sung by Dave Guard & The Whiskeyhill Singers

Poor Wayfarin' Stranger sung by Dave Guard

First Kiss with music by Newman and sung by Carl Fortina

Careless Love by H.D. Handy, Martha Koenig and Spencer Williams, and sung by Judy Henske and The Whiskeyhill Singers

A Railroader's Bride I'll Be; music by Newman and sung by Judy Henske

No Goodbye written by Alfred Newman, and performed by Laurindo Almeida and Carl Fortina

Shenandoah (again), this time performed by Tommy Morgan

Miss Bailey's Ghost performed by Imogene Clark and Carl Fortina

So, in other words, just a couple songs