Can you picket a car dealership?

You may hold a demonstration on any public land, provided you satisfy all local and state ordinances to do so. Public land is the road easement outside the dealership.

Something else you might want to consider, is posting yourself outside the dealership on the sidewalk out front, by the main drive with a sandwich board sign listing your grievances. This should require no permits, as you have full and free access to all public property, PROVIDED you are not breaking the peace or causing a public nuisance. Keep in mind that most local jurisdictions have anti-loitering laws--provided you keep moving, legally you are not loitering.