Inca Empire is able to expel Spaniards neither any other power too be able or intrested conquer that and so the country survives.
Iroquois Confederacy is able to survive until modern day.
In Central America some Maya city could survive much longer. In OTL last Maya city fell on 17th century so it not be total impossible.
Or then in Amazonia is unknown city state which anyone haven't found.
But this any can't be super power. Inca Empire can be local great power though.
Tawantinsuyu's downfall is an IRL example of Murphy's Law; a stabler Empire could've easily avoided outright conquest by the Spanish; it would've surely felt Spanish influence, but it would've been to Spain what Bhutan, Nepal or Tibet were to Britain.
The Mosquito Kingdom is one of the easiest to create without disrupting the rest of history too much.
The Mayan State of Chan Santa Cruz or Crusoob is another one.
Both of these states had British backing at some point.
Another possibility is in Araucania and Patagonia. I don't know if the kingdom founded by Orélie-Antoine de Tounens would could, being founded by a Frenchman and at, but his legitimacy came from his Mapuche supporters and I imagine his dynasty would intermarry with Mapuches if it survived. Otherwise, the region maintained a Native American majority and remained unconquered for quite some time, so another foundation is possible.
The last easy suggestion is an independent Greenland, or should I say, Kalaalit Nunaat. It would have an indigenous majority and leadership.
A more difficult proposition is an independent Mohawk reservation based on the Mohawk lands of Quebec. This microstate might have come into play if Quebec became independent in the 1980's, as the Mohawk leadership considered seceding from Quebec after its hypothetical independence and the leadership of Quebec at the time seemed game to let them go.
In some ways, Paraguay is sort-of like an independent American Indian nation, as the Guarani cultural, linguistic, and genetic influences are a deep part of its roots.
I wonder... the survival of the Inca Empire has been deemed very likely by everyone on this thread, but how would Tawantinsuyu develop next to the Spanish? The ruling class would probably find the Latin alphabet very useful, for administrative/bureaucratic purposes and as a tool to spread the Quechua language throughout the empire even more thoroughly, but the adoption of Christianity would undermine the power of the priestly class and that of the Sapa Inca himself, and the adoption of a monetary system would shatter the centrally planned economic system on which the state depended. *
Any takers?
* A system that, to me, has always looked like a hybrid between communism and feudalism; what if some visionary Spanish theologian saw in Tawantinsuyu's economic system a way to make all of mankind equal before God, to get rid of the diabolic influence of money, and to eventually get burned at the stake for heresy?![]()