Try a google search using "multicultural songbooks for children".

The first hit was www.songsforteaching.com:

Multicultural Song Books
for Children
Folk Music from Around the World


Bridges Across the World: A Multicultural Songfest (With Audio CD)
          Sarah Barchas


Colonial and Revolution Songs With Historical Narration (American History Through Folksong)
          (With 2 Audio CD's) Rusty McNeil, Keith McNeil


'De Colores' and Other Latin-American Folk Songs for Children and
Diez deditos: 10 Little Fingers & Other Play Rhymes and Action Songs from Latin America
          Jose-Luis Orozco


"Fake Books" from Hal Leonard Publishing Corporation
          The Celtic Fake Book
          The Folksong Fake Book: A Collection of over 1000 Folksongs from Around the World
          Gospel's Greatest Fake Book
          The Ultimate Country Fake Book


From Sea to Shining Sea: A Treasury of American Folklore and Folk Songs
          Amy Cohn (Editor)


Hush Songs: African-American Lullabies
          Joyce Carol Thomas


International Folk Songs
          Melody Line, Chords and Lyrics for Keyboard, Guitar, Vocal


Let's Make Music!: Multicultural Songs and Activities: An Interactive Musical Trip
          Around the World -- Jessica Baron Turner, Ronny Susan Schiff


Lullabies Around the World: Multicultural Songs & Activities
          CD/Book   Cassette/Book   -- Sara Jordan


No More! Stories and Songs of Slave Resistance
          Doreen Rappaport, Shane W. Evans


Sing 'Round the World, Volume 1 and Sing 'Round the World, Volume 2
          Shirley McRae


Sing Through the Day: Eighty Songs for Children
          Marlys Swinger (Editor), Nancy McKernan (Illustrator), Brenna McKernan (Illustrator)


The Singing Sack: 28 Song-Stories from Around the World
          Helen East (Editor)


Songs from Around the World! (With Audio Cassette)
          Berlitz Kids


Step It Down: Games, Plays, Songs and Stories from the Afro-American Heritage
          Bessie Jones, Bess Lomax Hawes


We All Go Together: Creative Activities for Children to Use With Multicultural Folksongs
          Doug Lipman


We All Sing with the Same Voice
          J. Philip Miller, Sheppard M. Greene, Paul Meisel


What a Wonderful World
          Bob Thiele, Ashley Bryan, George David Weiss


The World Sings
          Memphis Orff Teachers


Poetry
I, Too, Sing America: Three Centuries of African American Poetry
          Stephen Alcorn, Catherine Clinton


Words With Wings: A Treasury of African-American Poetry and Art
          Belinda Rochelle




Be sure to see -- and listen to -- our pages on
          Music to Build an Appreciation of Diversity
          Songs in French, Spanish, and Other Languages


See also:
          Bilingual and Spanish Books: Poetry, Rhyme, and Songs for Children