The following documents are required to prepare for either renting or purchasing a car:
Rental contract required documents
Required purchase contract documents
Residence card
Seal registration certificate
Residence record (confirming you live in the area)
Registered stamp (hanko / inkan)
In Japanese:
賃貸契約必要書類
・免許証
購入必要契約書
・住民票
・印鑑証明
・在留カード