If you live in an area with blue zone parking, your best bet would be to get a "macarron" from the city that allows you to keep your car in a blue zone for more than the legal limit of one hour. Only available for residents of the specific area.
http://www.lausanne.ch/view.asp?domId=61782&language=E
If there is not much in the way of blue zone parking, your next best option would be to rent a place in a building near where your live. The best way to do this is put up posters on poles with your contact details in the area you would be willing to accept a spot. You could also call some of the Regies to see if they have something.
Your last option, and your most expensive would be to rent a spot in one of the parking garages.