Audio (Quick) Can't use songs?

This question is easy to answer with an internet search. You may not use copyrighted songs -- regardless of whether they are nursery rhymes, carols, etc.

For example, many older Christmas carol are public domain, while some newer ones are still under copyright. The same is true for most nursery rhymes. Most are hundreds of years old, and long since in the public domain.

Just remember that you can't use a performance by someone else, even if the song/rhyme itself is public domain. Because their performance is copyrighted. So you must record your own version of that public domain material.