The most common option is to leave a deposit on a credit card. This must in any case be issued in the name of the primary driver. The amount for the rental car deposit is normally initially blocked on the card and only debited in the event of actual damage.
Please also check whether you have a PIN for your credit card.
Prepaid and non-embossed debit cards (Visa-Electron etc.) are not accepted as credit cards. On these cards, a sum of money can only be debited, but not blocked. As such, they are not suitable for leaving a deposit.
Important: If you are not sure whether your card is a fully-fledged credit card with a monthly credit line, ask your bank early on.