There's pretty much nothing outside of the Andes and Mesoamerica which could succeed long-term, and as time goes by any rebellion won't be an indigenous led one. The main issue everywhere else is the low population density and in general the low numbers of people of that group.
For the Mapuche, I don't see why at some point they wouldn't be grinded down by the Argentines and Chileans as in OTL. Both were modernising nations with much immigration and a need to expand. Who will protect them? The British or French, who might also want their land (although they'll treat them better maybe on the level of the Maori)? It'll piss off some otherwise reliable allies in Latin America to declare a protectorate over land which they claim, which would make it unappealing. Although in terms of mid-19th century American Indian groups, they're definitely the most likely to succeed by far outside of Maya, if only because for every other American Indian group, it was only a matter of time before they got smashed by the overwhelming numbers and industry of Euroamerican nations.
In the Americas, the Yucatec Maya ran their own rebel government for most of the 19th century. So a Yucatan state is really the best bet. I think a Neo-Inca country in the Peruvian highlands is also plausible given the whole Tupac Amaru mess in the 1700s.
The rest are kinda problematic because their low population densities, making it impossible to domesticate epidemics, mean they're likely to be overwhelmed by the sheer flood of Europeans. Some successes are possible for decades, even centuries, as the Pueblos or the Abenaki or the Mapuche showed. But once a European foothold is successfully established--and by the 1640s they already have been--in the long term, and definitely by industrialization, colonial society will expand and the indigenous world will contract. This is the case for both North America and the Southern Cone.
OTOH Paraguay's main language is Guarani, which is actually more widely understood than Spanish. Brazil could plausibly have turned out similar and become a Nheengatu-speaking country. I dunno if you consider these "native" nations though.
Yeah, an early POD is the best. But once Euroamericans have a foothold (as the Anglos did by the late 17th century), it's going to be insanely difficult for any native group to survive independently. People like to cite the Proclamation Line and Britain making an American Indian protectorate, but I don't see why that wouldn't be abolished at some point and Euroamericans grab the land, even if the result for the native peoples there is less horrible than in OTL.
Nheengatu would've taken an early POD, although it would be a very interesting signifier of Brazilian identity. But wasn't Nheengatu a simplified version of the original Tupi language? Guarani is also interesting. But in both cases, it was widely spoken by both indigenous people and mixed-race people, who made/make up the majority of the population. And if the majority of the population is of indigenous descent...