I actually drafted a timeline on this but never got around to making anything of it :
In the 1830s Brazil's Southern Rebelion in the South
http://en.wikipedia.org/wiki/Riograndense_Republic ends with the collapse of Brazil. Some European power moves in to the former Portuguese Guyana ( in reality just taking control over the mouth of the amazon ) opportunistically while every other South American country engorges on minor territorial claims on Brazil. Uruguay gets a sliver and Paraguay probably gets part of Mato Grosso while the South goes independent and the interior largely lawless.
From here Paraguay courts the rump of Brazil so that if its not openly friendly, it is at least neutral. Having the Peru-Bolivar Confederation emerge intact against Argentina and Chile will do wonders too. Then have Chile really push claims in Patagonia (since it won't be able to think about taking Bolivia's coast) while at the same time putting Argentina into a financial crisis and surrounded by enemies.
Now Argentina, surrounded by Paraguay, Riograndese, Uruguay, Chile, and Peru-Bolivia does something stupid to solve a financial crisis like charging exorbitant tolls on the Paraguay River or preventing any goods from entering Montivideo from entering into the rest of Argentina (the later was done OTL to ensure Buenos Aires remained an important port). Combine with the prospect of foreign debt collectors in the form of gunboat diplomacy ( the French Blockaded Buenos Aires OTL for a time to get debts repaid ) and you have a situation where Paraguay can win.
After Argentina does something stupid to provoke war with Paraguay ( said tolls ) war begins with a large coalition against Argentina. Have Paraguay do really well with an amazing general who takes Buenos Aires and then demand negotiation.
Paraguay can get everything on the North / East Bank of the River Parana, Chile can get territory in Patagonia, and Bolivia territory in the NorthWest. Buenos Aires is firmly on the other side of the river as well are all of Argentina's major cities. Argentina loses valuable land, but not greatly valuable and not the majority of its population or capital like people imagine.
France and Britian will probably not allow Uruguay to be absorbed by Paraguay via coup backed by the Colorados due to the economic situation by having the staple-port system between Montevideo and Buenos Aires endangered by Paraguayan Hegemony.
Then since the timeline continues for a Paraguay Wank, Paraguay ends up grabbing the Chaco and Mato Grosso from Brazil and Bolivia, and ends up absorbing Uruguay anyway, but this would be in the future.