Possible candidates and scenarios.
Well there are enough heads to fill crowns or asses to warm up thrones. The concept of breaking up the Spanish Empire and sitting sovereigns on each had already been brought up during the reign of Charles III. After the Wars of Independence, Bolivar thought an absolute monarchy would suit Peru. Additionally there is the actual example of the Portuguese monarchy being exiled in Brazil, and the positive effect it had on Brazilian history. So with that said the actual break up took place between 1811-1815. There was the idea of having Carlotta Joaquina set up shop in present day Argentina, but her husband put a stop it, and with good reason too, given her character and reputation.
Around that time there were four areas which merited a viceroy : Mexico (Central America), Peru (Peru, Ecuador), La Plata (Argentina, Bolivia, Paraguay, and Uruguay), and New Granada (Venezuela, Colombia, parts of Ecuador, Panama, and parts of Central America). The Philippines, Cuba, and Puerto Rico being Captaincies. So we've got 4 seats to fill.
Let's call the main breaking point, Ferdinand VII's abolition of the Constitution of 1812. So this sets off, the Wars of Independence.
Back in Europe, its an everyman for himself situation. Ferdinand VII didn't inspire too many positive feelings towards himself, even in his own family.
So there are plenty of candidates willing to roll the die.
First there's dad, Charles IV is still hanging around, going into exile in Rome. Say he gets sick of being cuckolded by his nagging wife. He could always hop onboard a ship and head off for a tropical get away. He knows its plausible, since his daughter's off in Brazil. Where would he go? Probably the most loyal outpost, Cuba, just as a gathering point for any Loyalist forces that want to rally around. In OTL, Cuba ended up as a final destination for plenty of Loyalist, which is why the rumblings for independence were delayed til the 1860's.
Maybe Charles IV, is too tired or old, but then there are still plenty of other plausible candidates. First there are Charles IV's two other sons, Carlos (from whom the Carlists spewed) and Francisco. Carlos was old school, believing in the divine right of kings and all, but was also a dutiful man. Carlos allowed FVII to sideline him, and only initiated the Carlists Wars because of a sincere belief it was his God-given duty to rule. Seeing the possibility of establishing himself on a New World throne, not as an act of rebellion, but as a continuation and preservation of Bourbon family rule, he might. Given his temperament Carlos would be suited for Peru or Mexico if he can wrench it away from Iturbide. If not there's always Francisco. He was offered the possibility of setting up shop in Buenos Aires, but did not receive any positive encouragement from Charles IV. Well assuming this time around Charles IV took some initiative, then viola, you've got a kingdon in Buenos Aires.
Francisco and Carlos would constitute the most legitimate and ready made candidates for Bourbon thrones in the New World. Assuming we're sticking to the Spanish Branch or direct descendants of Spanish monarchs, then there are even more options. I'm sticking to male descendants only, because they would be the most palatable candidates to most Royalists. Having seen how pointless backing a female candidate was during the Carlota Joaquina episode. There are Luis Maria de Borbon y Vallabriga, grandson of Philip V; then there are Infante Sebastien of Spain and Portugal, as well as Infante Miguel of Portugal, both are great grandsons of Charles III.
The craziest candidate being Don Luis Maria, at the time he's a clergyman in Spain. However, Don Luis Maria's father Don Luis, had been a clergyman and traded in the red (archbishopric) for some pink (wink, wink), why not trade in the red this time around for some purple (throne). Don Luis Maria was the only member of the royal family to remain in Spain during the Napoleonic Wars, and acted as regent for Ferdinand VII, while FVII was in exile France. When FVII disbanded the Cortes and abjured the 1812 Constitution, his actions impacted Luis Maria negatively. Luis Maria, through reputation, cooperation with the Cortes, and as a supporter of constitutional monarchy would if he had chosen to risk it made an ideal candidate for a monarch.
Don Sebastien and Don Miguel were already in the New World at the time the revolutions took place. Given the distance and time it took to travel between Europe and certain parts of the Spanish Empire, both make ideal candidates. Don Sebastien at the moment is an infant, but his mother Maria Teresa is a scrapper, having fought for her son's hereditary rights in Spain in the OTL. Well in the ATL, what's to stop Maria Teresa from accepting a regency for her son. As a daughter of Carlota Joaquina, she could lay claim there, in addition her father, John VI, who could offer material support was running Brazil and comfortably installed in Rio.
Dom Miguel is pretty much in the same boat as Don Sebastien, except of course, he's Carlota's boys. Assuming Carlota renounced her rights in favor of her younger son, then Johnny boy might have been more amicable towards setting up a kingdom in Buenos Aires. There eldest, Pedro was already an adult and by 1819 a father..... so Miguel could have already been expendable.
Either one of these alternate candidates could set up shop. Additionally, any one of the more charismatic princes of either Bourbon-Parma or Bourbon-Naples could've jumped ship to the New World, planted a flag, and taken a roll of the die.
The fact that Spanish America was essentially conservative and Catholic played into there hands. Other than regionalism within the prospective Kingdoms, the assumption of a King in anyone of the Viceroyalties, would have kept a lid on strife for at least two or three more generations, as was proven in Brazil...... or as mentioned earlier when large numbers of Loyalist from OTL, emigrated to Cuba and squashed any budding hope for independence for another 40-50 years. The real trick to survival is adaptability and the transition/abolition of slavery.
