What Cannonfire said
Lots of revolutions have occurred non-violently. Of course, much depends on how you define the word "revolution." For my part, I would say that FDR's New Deal was revolutionary, as was the fall of Communism in Eastern Europe. Nazism was a revolutionary doctrine; although preceded by years of street violence and assassinations, the actual Nazi takeover occurred more-or-less legally. The granddaddy of all bloodless revolutions was the Glorious Revolution of 1688, which saw the downfall of King James II of England.
History gives us the many iffy situations. Was the collapse of the Second Empire a non-violent revolution? It took place during the Franco-Prussian war, right after Napoleon III was captured at the battle of Sedan. His government, run by his wife, might have stayed in place, had it possessed any popularity. It did not. The Empress ran off to England a few days after the battle and a Third Republic was proclaimed -- with no shots fired, at least not in Paris.
You could argue that the establishment of the Second Empire was a bloodless revolution: Napoleon III, having been elected head of state, decided that he liked the job so much he would just, you know, keep doing it. Nobody mounted an armed challenge, although a lot of people reacted as though the whole thing was in terrible taste.
The Civil Rights movement? Interesting case. Martin Luther King was, beyond doubt, an apostle of non-violence. But much of his power derived from the unspoken realization that if King failed, those favoring violent approaches would step forward. (Of course, everyone knows that violence was employed by those who despised what King stood for, but that fact isn't relevant to our present argument.)
One could say something very similar about Gandhi. His passive resistance worked. But many would say that what the British really feared was the threat posed by non-pacifists, such as the Indian National Army.
Well, one could go on and on along these lines. ....
I've said it before and I'll say it again: The only revolution that stands any chance of succeeding in this country is a fascist revolution -- and that's one which I do not want to see. We need evolution, not revolution.
Like I've been saying: "Slow politics."