Well, I think there still would have been rebelions, cause there were a lot of profound reasons for discontent among all classes of Lain American society. And, if both the US and the French revolution have taken place, that means the Latin Americans have an importantant ideological and practical base for their claims. Would they succeed? I see three scenarios:
1) If there are still Napoleonic wars between England and France BUT no Peninsular War, Spain might remain a French ally. If this is the case, there might have been an ever greater British involvment in Latin America. IOTL, the British were friendly to the revolutionary movements, because these were against Spanish commercial monopoly and favoured free trade; but the fact that Spain was its ally against Napoleon (at least since 1808) discourage direct British support of this movements. If Spain isn't an ally but an enemy, these restrictions don't longer exists, and British may intervene directly.
So, in thjis scenario, I think revolutions are a must (if they don't start locally, they would be started from abroad by people like Francisco de Miranda, who disembarqued in Venezuela in 1806 with British support). And, if they British play their cards correctly (unlike what they did in Buenos Aires), these would probably succed, and Spain would loose, because it would be very hard for her to fight both the revolutionaries and the British.
By "play their cards well" I mean clearly stating that they want to "liberate" these lkands, not anexing them.
2) Spain is a British ally. If this is the case, I think revolutions would still arise, but it would be much harder for them to succeed. Specially if Spain had allowed British ships to trade freely in Latin American ports, which would leave Britain with almost no reason to support any revolutionary movement that appears. Instread, it might side with the Spanish and help them repress them. Spain might be able to retain her empire or a significant part of it for a long time, until local rebelions and the lack of industry in the mothercountry make it too costly to mantain.
3) Spain is neutral. Britain still has an economic reason to support the rebels. But Spain is in better shape to impose her rule and the revolutionaries lack an excuse to start the rebelion (their King is no longer in jail). But, since the detention of the King was nothing more that an excuse to spark the rebelion, another might have replaced it. Revolutionaries might have had a harder time in TTL, but I think that, if they still rebell, they may still triumph. Why? Because, given the Spanish authorities intolerance, once a revolution had started, the rebels had no choice but to suceed or be excecuted. And this was a powerfull incentive to succeed.