Redbones? Rare?
Redbones are about as common as dirt in many parts of the country. Any place south of the mason-dixon line (or west of the Appalachians) is going to be crawling with redbones and redbone breeders of various types. Is your heart set on buying from a breeder? These wonderful hounds languish in shelters by the thousands all across the country. They go stray a lot, and for some reason (that was discussed in a long thread a couple weeks ago) no one adopts large hounds.
I doubt that you'll find a non-working breeder of them who's of any quality though. These are one of the few dog breeds left that people still raise an eyebrow when you say you want one as a pet. A lot of people wind up with them as pets, but very few people actually breed them with that in mind, and anyone who did I'd find very suspect.
Redones are not an AKC registerable breed. Most redbone breeders register with UKC and the UKC has an extensive coonhunting program. The reason to register a redbone is to hunt him or her, not to have a show dog. Coonhound events do have bench shows where they conformation-show the dogs, but it's kind of not really the point, just a side thing.
If you really want to buy from a breeder, first, prepare to get shot down a lot by breeders who think that if you aren't going to work your hound, you don't deserve to own one. Then find a breeder who doesn't care that you won't work their hound, and get a pup they think is showing low drive but still has a solid temperament. One of the things to recommend a good working-line hound is this very solid, very steady, bomb-proof temperament. Working hounds have to have it. They have to work in close proximity with other hounds without loosing their heads, they have to remain focused on their task without letting other stuff bother them. My working-line hound (adopted by me as an adult--and I do not hunt) is completely unflappable (except for car rides--he hates riding in the car but no one is perfect and that's his little quirk).
Honestly, I'd really look closely in to rescue. Many of the dogs who wind up in rescue wind up there because they have the exact qualities you're looking for: they are pet quality, not working quality. That's why they are looking for a new home. There are hound-specific rescues all around the country with hounds of various ages, from young adolescents and puppies (you'd be shocked at the number of hounds that wind up in shelters already pregnant) to older dogs looking for a nice comfortable retirement home, and everything in between.