I think multiple PODs are needed:
Find a way to develop the countryside in a lot small establishments run by a rural middle class instead of fewer larger establishments run by a rich elite. Maybe the process starts, and keeps going, by the mid 19th Century as a way to shield the larger establishments against the Mapuches, as Rosas intended: give the frontier lands, more likely to suffer raids, to anyone who wants them, so raids into his and his buddies lands, are diminished.
Over time, this develops a larger rural middle class, erodes the power of the rich elite, and develops a larger and richer internal market for the rise of light industry. A less powerful upper class can also reduce the likehood of coups while the pressure of a larger middle class can improve the election process early on.
Bonus points if, while all this happens, the forty years of intermittent civil war are shortened or avoided altogether. GDP per capita is estimated to have remained the same during those decades, and about 50,000 people are estimated to have died, out of a population of less than a million. Displaced and seriously injured people ought to be added to that.
This might also cause earlier public education politics, increasing alphabetization early on.
By the mid 20th Century, we should still have internal strife and killings, but probably no military coups. Instead, we'd have an uninterrupted history of increasingly more legitimate elections dating to the 1820s. There is also a larger light and cultural industry going on. The key issues here to deal with the social conflict and balance heavy, defence orientated industries and profitability. Essentially, some sort of smarter Peronism. Bonus points if it deals with the social conflict without co-opting the unions and using corporatism.