Because of Argentina's state Argentina will naturally drift towards you without a coup because of the ruling party type (black/gray ruling party types naturally drift towards the Axis). Coups are only necessary if the state is *already* in a faction (a coup will remove them from the faction) or if they're a state type that doesn't hold elections which is unfriendly towards your government type.
Now you won't be able to have their territory outright - there is no intelligence based option that will give you that, but you can make them a member of the Axis fairly easily.
Step 1. Trade with Argentina to 200 relations as QUICKLY as you can (don't want to have convoys going out after Sept 1st 1939 or it'll cost you a fortune).
Step 2. Fill Chile with spies and set them to Raise Threat - because Chile will have a blue government type the threat raising will work really well on Argentina dropping their neutrality so they'll join you. Also Chile doesn't have a ton of LS so your spies shouldn't die very much - you could likely get more play with raising threat on the USA, but they'll kill your spies a TON and it will end up costing a fortune - so I'd at least run a test game trying with just Chile.
Step 3. Diplomatic influence. Now, because you're running lots of trades, and their government type already likes you, even if the USA tries to influence them back they'll still drift into your corner, and because of the threat of Chile, they should be far enough into your corner and low enough neutrality to join you very early
Sometimes they naturally end up in the Axis if a Democracy or Communist state are really racking up threat.
The only thing I'd worry about is they *may* get invaded by the USA when they finally join the allies and DoW the Axis, before you're ready to go to the Americas, but they may not.
You could also potentially do the same with Peru and Brazil since they both have similar ruling government types and will also respond to Chile's threat (although Brazil does have an event that may change their government type slightly in some versions).
Peru could be really handy because they'd give you a base to operate from in the Pacific - which would make an invasion of both US coasts by way of South America possible
