It is not that hard, really. Gotland, Dithmarschen and Jämtland were independent peasant republics where all matters were settled at the Thing, including making and reversing laws. All free, non-peaceless (men could be declared peaceless for crimes, which meant anyone could harm them without reprecussions) had a vote at the Thing.
Gotland were nominally the subjects of the Swedish King, but did not pay taxes and had no royal troops stationed. There were no nobility or feudal levies either, only the local citizens (note that Gotland does not include Visby, which was a free Hansa city). The plague hit Gotland very hard, and when Valdemar of Denmark arrived with a modern mercenary army of heavy infantry and knights (of German and Frisian origin) in 1361, he crushed the two peasant levies raised to fight him (note that peasants were required by law to own arms and armour and train with them, so it was no rabble) and captured Gotland. Have Valdemar turn his attention eslewhere, the plague not hitting Gotland as hard or a lucky shot from one of the peasants take Valdemar out, and Gotland could very well survive as a peasant republic.
Jämtland was completely independent until Sverre of Norway conquered it in 1187 - it was a fluke - the Jämtlanders raised almost 1200 armed men to fight the Norwegian King and his Hird of 100 men, but during a night battle the Jämtlänningar started fighting each other by mistake in the darkness. Have Sverre lose the battle on the ice of Lake Storsjön and Jämtland could survive - after the plague, Norway would be too weak to take it by force, and the Danes and the Swedes are up to their ears fighting each other.
Dithmarschen was a de facto peasant republic in Schleswig-Holstein that lasted all the way until 1559, so it actually fulfills your challenge without any edits of history.
http://en.wikipedia.org/wiki/Dithmarschen#History
