How about this: the first independence plan of Belgrano is accepted by the Argentinians, and Francisco de Paula de Borbón, son of Charles IV of Spain, is made king of the United Kingdom of Rio de La Plata, Peru and Chile. He still marries his niece, Luisa Carlota of Two Sicilies, and they have a son, Enrique.
In Brazil, everything goes like OTL with prince Pedro marrying Leopoldina of Habsburg and later becoming Emperor of Brazil. South America is dominated by two big monarchies. But here he has three surviving children: Paula, Pedro and João.
When John VI dies in Portugal, Pedro I takes the young prince Pedro with him to Lisbon, in order to fight with Miguel for the throne. He wins as OTL, still dies around 1834 and his son is crowned Pedro V of Portugal.
In order to keep the peace with the kingdom of La Plata, Paula is married to Enrique, and they have a son, Francisco. After a period of regency, the young Prince João is made Emperor of Brazil in 1845.
However, in 1850 the epidemy of yellow fever in Rio kills the young Emperor, who dies childless. There are only two heirs of the throne of Brazil: Pedro V of Portugal and the young Prince Francisco of La Plata. The Brazilians do not accept it, and proclaim the Republic. Enrique I of La Plata decides to go to war for the rights of his son, and invades Brazil, while Pedro V of Portugal doesn't accept both the Republic and Buenos Aires taking over the Empire, and decides to annex Brazil as a United Kingdom again. Spain supports Enrique, and invades Portugal.
After some time, the forces of Enrique wins, and is proclaimed the Empire of South America, which consists of the kingdoms of La Plata, Brazil, Peru and Chile, in personal union under Francisco II de Borbón. The war would be known later as the War of South American Succession.