These animal tales appear in literature from many countries, some ancient. Aesop, Androcles, De La Fontaine, even Ambrose Bierce tried his hand. Joel Chandler Harris gave us the tales as told by African-Americans, and enriched our literature.
Ugh, Stilly River Sage, you speak false! The American Indian fables did not become known to the world until the 20th c. Cushing and others were collecting in the 1880s, but most publication was after 1900. How could Harris have given credit?
I see one of these books on the shelf in front of me; the excellent "Zuni Folk Tales," 1901, F. H. Cushing, reprinted by the University of Arizona Press. He includes one tale from the Italian that entered Zuni oral literature, "The Cock and the Mouse." Undoubtedly some tales from De La Fontaine entered African-American oral literature.
Like other peoples, the Indians had their trickster tales; coyote being the trickster in many Navajo tales. There are several books, perhaps the best is by Haile, 1984, "Navajo Coyote Tales," Univ. Nebraska Press, but there are others, some in children's editions.