I am not very well acquainted with the Balkans in the 19th Century, but my guess would be that it is unlikely that any indigenous Republic or Kingdom could spring up in the 19th century. The revolts against the Ottoman Empire that broke out throughout the century were driven by nationalists who wanted their own nations, not federal states. While the "new" Balkan states such as Bulgaria, Greece and Serbia could cooperate for a time against their common enemy, the Turks, once that threat was lifted they were soon fighting each other. Unification of the Balkans under Russian, or even Austrian hegemony would be far more likely.
That being said, if Karageorge of Serbia had managed to hold on to power during the Napoleonic era, he may have been able to unite the various Balkan principalities under the banner of Orthodox Christianity vs. the Turks. If I recall Karageorge was affiliated with the Hetairia, a Greek Secret Society/Independence movement. Such a kingdom could have united most of the Slavic Christians against the common foe, and at this stage in history might been more appealing that the other nascent nationalist movements that became more popular during the 19th century. So if a strong and stable state developed under Karageorge starting in 1805, and if this state remained viable, or the Turkish threat severe enough, such a union may have endured into the 20th century. A