There aren't many Native Americans in Hawai'i, actually. Along with blacks, it's pretty much the only ethnic group that Hawai'i does not have a significant number of.
These states have American Indian populations higher than 2% of the population:
Alaska - 15.6%
New Mexico - 9.5%
South Dakota - 8.3%
Oklahoma - 7.9%
Montana - 6.2%
Arizona - 5.0%
North Dakota - 4.9%
Wyoming - 2.3%
Basically, there are only a few states where Native American populations are high enough to make the difference in anything other than a razor-thin election. In addition to low percentages in most states, Native Americans are less likely to vote than other populations for self-evident reasons.
Native Americans are generally economically liberal, with a large range of social views. In general, they are quite Democratic, especially on reservations. However, in Alaska, some vote in hopes of oil industry activity and thus vote Republican.
As for your question, there simply isn't an area with a significant enough Native American population in Oklahoma to elect a Native American very easily. There is probably no county in Oklahoma where Native Americans cast more ballots than whites, at least.
Well, I was kinda including thinking Hawaiian natives as native american...though, of course they're polynesian by ancestory...they're "native" to Hawaii...
As I recall Oklahoma's native American population is traditionally Republican... I wonder if there's still lingering R-party support among the populations there...
Actually, it seems to me that if Rep. Dan Boren's district were split into two and there was a Northern OK district that included bits of Tulsa and a little of Wes Watkin's CD where there are significant native American populations, a CD would be created with a very significant Native American population and a Democratic edge... the cd might kinda look like Carson's old cd used to, though, adding Dem-leaning parts of tulsa.... Meanwhile, the southern bits of Boren's cd could be combined with dem-leaning counties in Tom Cole's cd to recreate the "little Dixie" district for Boren to keep...
In New Mexico, it seems to me an optimal Dem gerrymander would add more of the southeastern counties to Udall's district, so that it becomes less heavily Democratic-leaning, while adding Northwestern areas to the CD in the South to make it a plurality Latino/Native American district...