Your POD is after 1900?
I'd go with:
No 1930 coup. It was a close affair, and many in the military were hesitant. Averting it should be able to butterfly away the rest of the 20th century coups.
No WWII. This keeps the USA from becoming a (half)world hegemon and keeps the Marshall Plan from screwing Argentina's exports to Europe. At this point, Argentina would remain a quasi-colony of the surviving British Empire - but the expiration date of the Empire has only been postponed, not erased.
Two things happen: First, without WWII Argentina movie industry remains one of the top industries in the Spanish speaking world - the problem is translating this to exports from another sectors of the economy. Eisenhower praised how American cinema opened the gates for a lot of American products abroad, but Argentina would still lack the diversified economy to take advantage of in movie advertisement (this is still just before TV) and import substitution industries won't cut it in the broader world.
The other point is that, as a quasi-colony of a British Empire who's friendly, but not aligned to the USA (and decolonization is going to bring discord between them without WWII to weaken the UK), Argentina would contest American influence in the Southern Cone as a matter of fact. It could even try to keep propping the idea of the ABC powers. The key here is navigating the transition to a post British Empire world as well as to a diversified economy and, eventually, to the information age.