What if Napoleon won Waterloo and the battles after that...

There's simply no way Napoleon could have found peace on his throne. The moment the Allies refused his peace offers upon his return from exile in 1815, he was doomed. Sooner or later (but likely sooner) he would be off the French throne once again. Napoleon had never faced as many enemies at once as he did in 1815. Even if he had have won Waterloo (which was entirely possible) that's no guarantee the British and Prussian armies would have been destroyed. Even after Austerlitz - Napoleon's greatest victory - the Russian army was still very much intact and Napoleon spent months and another whole campaign trying to chase them down and finish them off. So even a victory at Waterloo wouldn't guarantee the destruction of the British and Prussian armies, and while pursuing these retreating armies he'd also have to prepare to fight the combined might of the Russian and Austrian armies, and the possibility of a Spanish invasion of France from the south. I think the general consensus is that it's very unlikely Napoleon would be able to pull off another Austerlitz in 1815. His health was getting steadily worse and his good judgement was slipping more and more frequently.

But okay, even then, let's say he somehow defeats all four major Coalition powers - a near-impossible thing to do. At best, they would make a peace that would last for probably no longer than a couple of years (like the Amiens peace), long enough for the Allies to rebuild their armies and prepare for another shot at Napoleon. So long as Britain was willing to subsidize their allies on the continent (which the past twenty-two years had shown was certainly the case), Napoleon would also be either at war or living under the threat of war. Despite the love and devotion his soldiers consistently held for Napoleon right till the very end, the Emperor's popularity was slipping back home in France (and especially Paris and other urban areas). The Senate was itching for any opportunity to get rid of him. Everybody wanted peace, not just a short-term truce, and over the past 15 years Napoleon had simply shaken up too much of Europe to be allowed to reign in safety and peace.

Possibly the final moment that a long-term peace in Europe for Napoleon's empire was feasible was the 9th of September, 1812; the day before he began the retreat from Moscow.

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Originally Posted by WhatAnArtist

Possibly the final moment that a long-term peace in Europe for Napoleon's empire was feasible was the 9th of September, 1812; the day before he began the retreat from Moscow.

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I'd say that the very last moment as far as 1812 is concerned, was September 7th. Had he committed the Guard as it was asked of him when things might have turned into a complete rout for the enemy, and the total destruction of the russian army, then and only then Napoleon would have truly succeeded for a very long time. But bad health conditions and the subsequent frustrations clouded his judgement for the entire fight, so he burned away his very concrete chance to end the war right there. Once tsar Alexander understood that his army was still mostly intact and the Emperor could be trapped by the winter there was nothing he could do to obtain peace anymore. He was destined to fail the day he entered Moscow.

But there were also other moments when he could have achieved a long peace, even later, in 1813. His initial victories against the Prussian and Russian armies at Lutzen ad Bautzen were very real defeats and morale hitters for the Coalition forces, as late as the first day of the Leipzig campaign, he could still have won, since there was a clear moment when the French forces were on the offensive and a huge gap in the Coalition armies was forcibly opened with powerful cannonades. Once again, he did not follow up the attack with a decisive push like he did a decade prior, had he done that, there was a very real possibility of him defeating a large portion of the allied forces, with undeniable huge morale loss across his enemies. Even at the last day of the Leipzig campaign, there was a chance for peace as the Coalition forces were exhausted and demoralized by the great resistance put up by the French, that were still holding the lines and were not moving from their fortresses despite all the enemies' attacks of the days prior.
It would be also good to mention IMHO the (clearly unacceptable, but nonetheless proposed) peace treaty of August 1813 that would have granted the Emperor rule over France and Italy and prevent the intervention of Austria in his affairs.

I think we are forgetting the sleeping lion in background. Whilst victory in Europe might have secured peace for a time, Britain was determined to ensure that Europe was not united either under Napoleon or anyone else, and as long as the Royal Navy ruled the waves there was nothing Napoleon could do to undermine Britain's wealth and prevent her funding repeated coalitions and wars against him. His biggest failure was not being able to break Britain's influence over European politic's.