This is a book I remember from my youth that I'd like to have for my
children.  The book's name is "Lullaby".  It's a small (32- or 64-
page?) book, well illustrated, with rhyming lyrics on every page. 
Glued to the back cover is a record with the book's lyrics sung to
instrumental background.  The book includes the phrase "Lutes, Flutes,
Guitars, and Angels" which may also be printed on the cover.  A place
to buy the used copy with record is ideal, though if I can find
pictures and an MP3 file I'd also be happy.  I'm 24 years old and I
saw the book when I was approximately 6-8 in a supermarket stand, if
that helps narrow down the publish date.

Hello.

Your book is "Lullaby" by Elizabeth Swados & Faith Hubley (Harper &
Row, 1980).

A bookstore listed at abebooks.com currently has the book for sale.
http://dogbert.abebooks.com/servlet/BookDetailsPL?bi=56607334
I called this bookstore (D&D Galleries, Tel. 908-874-3162), and spoke
to a person named David. He was kind enough to read the book to me
over the telephone. When he came to the phrase "Lutes, Flutes,
Guitars, and Angels," I knew this was the right book. Their copy
includes the record.

Other dealers that have the book (& record) listed on abebooks:
http://dogbert.abebooks.com/servlet/BookDetailsPL?bi=155910158
http://dogbert.abebooks.com/servlet/BookDetailsPL?bi=60227250
http://dogbert.abebooks.com/servlet/BookDetailsPL?bi=67918577

search strategy: abebooks, lullaby

I hope this helps.

He answered exactly the question asked, and gave all the necessary
details.  He even verified by telephone that the book was the one I
described!