Concerning Portugal, the economic center of gravity was moving towards Brazil by the late 1700s. The Tiradentes revolt put a lot of people in Lisbon in alarm. I need to check my sources, but if I recall correctly, the British were pushing to move the Portuguese court to Brazil even before Napoleon’s invasion, as way of keeping Brazil firmly in their control (through Portugal). After all, Brazil is much larger and richer than Portugal. So, they might move there if Brazil revolts again.
Spanish America is an entirely different affair. It’s divided in four Viceroyalties with their own set of challenges. New Spain and Peru were built on top of native empires, and unlike what the mainstream media tries to portray, the Spanish didn’t come here, wiped out everyone and started fresh, they integrated the native structures including the nobility, into Spanish, or more specifically, Castilian peerage. For the common people, life went on without much change during 300 years. There were even people as late as the 1850s in some remote areas in Mexico that still held allegiance to the King of Spain and stashed their share of the Quinto Real waiting to be collected by the Real Hacienda.
In my opinion, New Spain and Peru can be held almost indefinitely or at least well into the 1800s if and this is a big if, Spain is able to placate or bribe the disgruntled viceregal elite (the nobility and the merchants). They did the same with the native nobility in the 1500s, I don’t see how this is very different. These are the people that are stirring up trouble there and have the means to fund any revolt. No Napoleonic invasion would be keeping the status quo, which means the New Spanish and Peruvian are resentful of Spain because they are losing money (mostly on the opportunity cost of not being able to trade with the world). There are other minor grievances on the preferential treatment of Iberian born Spaniards, but if you want a royal commission, all you had to do is buy it, and the nobility and merchants of both Viceroyalties were extremely rich, even by European standards. It’s the lower tier of nobles and merchants that are upset about it.
Revolution is not born of some universal ideal; it is the result of someone with money, influence or awareness being mistreated by those in power, and in the course of human history, only a minority has had money, power or awareness. So, you need not to buy off everyone, only a few to keep things quiet.
New Granada and Rio de la Plata are different, mainly because they were not heavily populated when the Spanish came, and were economically weak, and in the case of La Plata, also very distant. Support of the Empire was low there, mainly because the feudal structures were not as entrenched, and their elites felt very mistreated because they were more geared towards mercantile activities than land based wealth (mining). You’ll end up with a Bolivar eventually. Spanish authorities in the early 1800s were very incompetent starting from the top – Carlos IV and his son Fernando. They’ll send armies and keep the coast, but the interior is impossible to control due to the hostile population and immense territory. They’ll bleed Spain dry and upset New Spain and Peru. Colombia and Argentina will win their freedom after a bloody war, like the US, with British support. I just don’t see the status quo holding there, particularly in La Plata, where smuggling was out of control. Any attempt to stop it will start a revolt, because again, those in power there are not going to stand being ruined by some idiot in Madrid. Want to upset anyone into action? Just mess with their purse, and you’ll see how quickly they react and turn against you.
The changes are obvious in hindsight, it’s not that the Empire can’t be maintained, it’s the people in charge in Spain at the time that make it really hard, if not outright impossible. Reform and any chance to have Spain keep its empire mostly intact in the 1800s died with Carlos III in 1788.