The songs I often sing non-stop to six-year-olds:
The Marvelous Toy
Waltzing with Bears
Rock Island Line
(All God's Critters got) A Place in the Choir
Jenny Jenkins (I don't sing the version in the DT)
The Cat Came Back
(Boom Boom) Ain't it Great to be Crazy?

Not soothing songs at all, but they may be good for cheering up!