It depends on how long or what you want the apartment for?

Alot, if not all of the companies require an Alien Registration Card before signing a lease agreement. The only one that doesn't require it is Sakura-House, but they require the information of where you are working or studying.

Actually, the requirements seem alot more strict than I first thought, I think unless you are either working or studying then you won't be able to get an apartment at all. So if you are not doing either then looks like you would not be able to get one.