Just ran across "Rhymes and Jingles," Mary Mapes Dodge, 1875; 272 pages of material for very young children. It is in the Univ. Michigan Making of America Books, Along with "Baby World" (same author, 300 pp.), Eugene Field's lullabys and much else.
http://www.hti.umich.edu/cgi/t/text/text-idx?c=moa;idno=AEK2756
Rhymes