In the pilot episode of Vegas (airdate: 9/25/12), Gil Birmingham plays a Native tracker. His role is to identify motorcycle tracks and say whether they happened before or after a rainfall.
Birmingham's character has only a few lines and doesn't say or do much. He wears cowboy-style clothes like the the other ranch-based characters, and doesn't talk "Indian style" (with a ponderous accent). The only Native reference he makes is to his grandfather's collecting a plant for medicine.
Birmingham isn't listed in the show's credits on IMDB, so I assume he was a one-time guest star. Still, it's a good portrayal. Natives need more everyday portrayals like this--even if it's unlikely anyone would've consulted an Indian in 1960.
For more on Native-themed TV shows, see "Eskimo Susie" in Saturday Night Live and Native Tattoo in Defying Gravity.