I'll have to go back and dig through some source material to give you a qualified answer. The origins of many of these Brer Rabbit stories are understood to originate in Faulkner's neck of the woods, with Muskogean speaking tribes, such as Choctaw, Chickasaw, Alabama, Creek, and further east to Seminole. Add to these sources Cherokee stories, according to one reviewer at Amazon. This from the "spotlight" review on The Complete Tales of Uncle Remus:
The stories combine folktale motifs brought from Africa by slaves with those of the native peoples of the south, particularly the Cherokee and Choctaw. Since both cultures had stories with animal characters, and specifically trickster rabbit characters, ethnologists have not been able to completely determine which elements are the African and which are the Native American. No matter, since the two cultural traditions blend together seamlessly.
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?
Are you somehow suggesting that the stories weren't known to blacks until a white ethnographer came along and documented them? I don't think you're that clueless to the ways that cultures naturally merge and share material, but you haven't given it much thought. Of course the fables were known--to Choctaws, etc. And to the people who lived near or with them, in particular neighboring, and often escaped slaves. This commingling of stories happened over the course of several hundred years. Only in recent times has there been any acknowledgement of the commingling of the black and indian cultures, because it was harder to detect, or people simply chose not to see. There is a conversation between Choctaws in the American Indian novel The Sharpest Sight that addresses this--it was written by a Choctaw/Cherokee friend who wanted to make the point about how the Brer Rabbit stories are mis-attributed. Whether writing novels or fine scholarship, Louis Owens always had things he wanted to teach his readers. He wouldn't have included this in his novel if he didn't have good evidence to back it up.
The nature of trickster stories is that they combine observable animal and human characteristics. Rabbits, coyotes, bluejays, squirrels, crows, and other animals, turn up again and again in different cultures. They routinely snatch Defeat from the mouth of Victory because it is in their didactic nature to teach how to get along ("do as I say, not as the trickster does, learn from his mistakes").
I have much of the source material as photocopies in files and books on my shelves. I won't drop what I'm doing to look for it, but I have a couple of good starting places that might provide shortcuts. One that I don't own, but probably have some material from, is John Swanton's Myths and Tales of Southeastern Indians. It originally came out in 1929 as a Bureau of Ethnology volume. Swanton wrote many books, some about discrete nations, others that were regional and more comparative in nature. If you go back and forth between some of these books of his you'll find a treasure trove of stories and citations to primary sources. I found this particular volume via netLibrary, but they've set it up so I can't do any cut and paste or printing of pages, so I can't pluck bits and paste them here. These stories involve rabbits, hares, terrapins, opossums, turkeys, snakes, lizards, coyotes, wolves, hummingbirds, racoons, and panthers, to name only a few. It includes many of the Brer Rabbit and Uncle Remus stories. The story of the Tar Baby (p. 68, from his informant W.O. Tuggle).
Another book that provides a good start on tracking down good source material is Swanton's Source Material for the Social and Ceremonial Life of the Choctaw Indians, originally published as the Bureau of American Ethnology Bulletin 103 (1931).
It isn't even a matter of conjecture where the Joel Chandler Harris stories came from, it's clear to anyone who has worked closely with American Indian stories. It's a matter of how long will it take the mainstream culture to catch onto what Harris was doing. The invisibility factor of minority and indigenous peoples has a lot to do with why this has gone un-remarked upon for so long, and it's a shame that they were played off against each other.