There is a very popular Primary song (Primary being the organization of the Church for children up to age 11) called "Book of Mormon Stories" that has a pseudo-Indian tune and beat. Mormons use the generic term "Lamanite" for all American Indian (or Native American to be PC) peoples as well as Polynesians to a lesser degree. The term is taken from the Book of Mormon. So I'm not aware of any references to tribes by their proper names.

I think there were a few more Indian-oriented songs published by the Church as part of the Indian Seminary Program, which was a course of religious studies specifically for LDS Native American youth. This would have been in the '60s and maybe '70s.