I will add two things:
1) The best way to get accurate tribal perspectives is simply to buy books written by and for tribal people. Some even have their own publishers and distributors. For Cherokee, there's The Book Publishing Company. Cut Bank Creek Press is Creek. Oyate seems more diverse. Similarly, a business by and for Native Americans is more likely to stock tribal publications. We're lucky to have a powwow store called Driftstone Pueblo within driving distance; in other areas you might find a tribal art gallery.
2) Pay attention to balance. The genocide continues today, which means that contemporary Native American literature is often depressing. This is a problem when depression and suicide run rampant on reservations (and are rising in the mainstream too). Those very bleak stories are true, but not complete. Unfortunately I have found very little written about healthy, happy tribal characters in today's world. The best you're likely to manage is mixing the realistic stuff with some of the better mythology. Reading only dark stuff about a culture -- however well it might reflect current experiences -- isn't good for anyone. What I'd really like to see are more stories about integrating modern and historic motifs or reclaiming lost things. One I remember fondly is "The Elk Tooth Dress," about a girl and her relatives making various choices about which cultural motifs to practice. And while it's a game rather than a book, Potlatch looks like a promising example of something that teaches traditional values and practices through a modern medium.
This stuff is why, when I write tribal characters, I try very hard to represent both the ups and the downs. The current issues are real and compelling, so you'll see struggles about discrimination, identity, and social acceptance. That's hard, so sometimes characters faceplant. But I want to show healthy, effective solutions too -- things that individuals and tribes have discovered to make life work better, preferably replicable ones based on tribal values rather than just assimilation.
Tell ALL the stories.