"Green Rocky Road", "Tennesee Waltz" and "Jock O'Hazeldean" all make good lullabyes, the latter two in spite of their adult subject matter.
Gary Davis' "Candy Man" goes over well with kids especially if you throw in some funny voices a la Dave Van Ronk.
Also Woody Guthries' "Take You riding in my car" "I'm gonna write myself a letter" (those are the first lines if not the titles) which are probably in the DT.