Mahmud II dying in 1807- I think that if the Ottoman Empire falls apart prior to the Congress of Vienna, that is the only realistic POD that would avoid some of the subsequent bloodshed in that region.
With the end of the House of Osman, the Serbs might be able to grab a large section of the Balkans. Add in a Greek rebellion and the Congress of Vienna. With these new Balkans states emerging it would provide thrones to put displaced German and Italian princes on. Serbia and Greece definitely. Maybe Bulgaria and Rumania.
The relatively bloodless emergence of Balkans' nationalisms, and then immediately tying those new nations into the European system, where they can be exposed to Western European liberalism, combined with 30 plus years of peaceful, independent development before the disorder of 1848, could all combine to create a less ethnically divided Balkans. The focus of western european nationalism on language could also result in broader national definitions- Muslim and Orthodox both speak Serbo-Croatian- thus all are identified as Serbs. With new monarchies who want to build relatively broad-based support, focusing on language would make sense.
As for what happens outside of the Balkans to the Ottoman Empire, Mehmet Ali gets himself recognized as the Sultan of Egypt, then procedes to seize as much of Syria as possible, and grab the Holy Sites. With control of Jerusalem and the Holy Cities, maybe Mehmet makes a pitch for leadership of the post-Osman Empire (since I don't think he has the military ability to make a real bid)?
There are still Girays and perhaps collateral branches of the Osman floating around the Ottoman Empire. The British at least would have an interest in a larger state being able to maintain itself in Constantinople, and could engineer the elevation of a British-backed candidate to the throne of the *Ottoman Empire.