I am current living in a capsule hotel and can i apply Alien Card with the Hotel address ?

If i'm not mistaken don't you need to only apply for an Alien card if living in the country for 6+ months? Since the Visa periods after 6 months require a reason (i.e not temporary visitor visa) i'm assuming you are either working/studying? If so I think having an somewhere more of 'stable' living, even if it's a short term apartment, hotel, guesthouse would be better when applying for an Alien registration card.

Capsule hotels, by their business nature, are only for very short term staying. Usually for when those who are working (or out drinking etc) have missed the last trains/buses and need somewhere to sleep.

I am finding a apartment, but i don't have Alien Card for apply... how should I do ?

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.