http://www.paradoxian.org/hoi2wiki/index.php/Argentina_strategy
I've never played as Argentina, but I've played as Brazil and easily conquered South, Central, and North America. They're both regional powers and are the only threats to each other in South America. Since South America is filled with jungles, mountains, and the Amazon River I suggest building marines, mountaineers, and calvary, (thats what I did for Brazil except I built light tanks instead of calvary) and if partisans are bothering the hell out of you just liberate some small countries to make it easier. If you decide to want those countries back just release them from slavery, (puppet control) then re-conquer them. Also the guide will help you even if it is HoI2 but I'd also follow Tuscans advice and not join an alliance. I also know that Brazil, and Argentina are different but its just an example.
EDIT: Also watch your belligerence, I didn't do that and I ended up fighting the US of A, and the Allies all alone with my weak puppet states.