Or making the 1960s a lot worse.
The Lost Decade is still my best bet for something along these lines (it's still the Cold War), personally. Even making the 1960s a lot worse is still going to leave some gaps - Costa Rica being an obvious one (and at that point nothing can be done to dislodge Costa Rica from that status - it's a special snowflake due to specific historical circumstances), as would Venezuela (petrostate wealth insulated Venezuela from the rest of Latin America until the 1970s, when things got crazy due to the 1973-4 oil boom) and even Chile (and ITTL with LatAm going through major convulsions, the Christian Democrats will ensure that their country remain a stable oasis of democracy, which even the Chilean Left would recognize that stability is more important than bold experimentation) and Paraguay under Stroessner (his dictatorship was probably the most secure of all the Latin American military dictatorships and thus would remain durable for this period). Everywhere else? I can grant the remainder being fair game, I guess.
But the Lost Decade was one which touched the entire continent to some degree (except Cuba) and made things a lot worse. As a result it's easy to ramp up the Lost Decade into something like Latin America's Great Depression and fulfill a Cold War-era storyline. With a Lost Decade POD, the Colombian armed conflict could be so bad that it could infect its neighbors (even making Venezuela a battleground) and interact with all sorts of other crazy shit in Peru and Bolivia (imagine FARC mixed up with either the MRTA or the Shining Path and things would get wicked bad indeed) and make Central America much worse than OTL. Combine that with the incompetence that was Miguel de la Madrid's handling of Mexico and his predecessor's absolutely insane attempt to defend the peso "like a dog" which backfired horrifically (and hence the beginning of the Lost Decade) and Mexico would thus be fair game for its share of revolutionaries and civil war. Brazil ending up under Médici and Costa e Silva-esque hardliners instead of someone like Figuereido (and hence no democratic transition) could potentially start interesting as part of a regional effect. And that's just for starters in terms of setting Latin America back several decades. Of course that would mean that the US would be interested in backing the weak newly-democratic governments, as well as the Central American military dictatorships and the Nicaraguan contras (the latter two OTL); the Soviet Union, despite whatever the propaganda machine can come up with, would have its priorities elsewhere as it deals more with problems back home. France, however, could have some interest in this region, and if only to ensure the security of its overseas regions in the Caribbean and in Guyane. The global economy would be absolutely fucked up, both in terms of the financial markets (where almost all LatAm countries have stopped paying off their debts) and in terms of the multinationals' subsidiaries in the region. Miami becomes more of the de facto unofficial capital of Latin America than it is (was?) OTL. Stuff that would be the object of nightmares, especially with the international Reagan/Thatcher context and the democratic revolutions in Eastern Europe - makes for an interesting contrast, n'est-ce pas?