I have been trying to rent a second cellar in my block for ages.  Regie cannot be bothered to do a contract and anyway they probably cannot rent an appartment to one person and a cellar to another (problems when changer renters)

Only way is to find an empty cellar in your block and discuss privately with the owner (Regie will give the name) or if there are no cellars free in your block put an advert in your local Migros or Coop

Alternatively there is a good webite called glocals but you would have to advise the approx location of your appartment so as not to waste people's time  

See with Geneva Free Ports & Warehouses. You could also join Le Cave, a club a wine amateurs where they rent storage space for wines (mostly those puchased here I guess) at a decent price. Last but not least, you may want to consider a wine cabinet such as Eurocave. How many bottles are you talking about?,

Or maybe you mean a cave (a grotte) - try the Jura or the Saleve. Good for storing cheese