What are examples of insurrectionary methods of resistance?

revolting or rioting

Rebellions were common throughout history, although they sometimes lead to full blown Civil War. A notable example would be the US Revolutionary War, which can be interpreted as a civil war.

Petitions, protests, and rallies are non violent/less aggressive approaches. Look into olive branch petitions. Protests happen all across the Middle East (Arab Spring), in the European Union due to the economic crises, and recently in the US Occupy protests. Rallies happened a lot during the cold war, especially in University Campuses. They're just as common today.