You must pay your state tax due using the state’s preferred method of receiving payment. For most states that will be by making a payment to the state’s own tax website, or by mailing a check or money order.
Can you purchase a money order to mail in to CA? Or can you pay by credit card? If you do not have a credit card, you could get one of those pre-paid cards for cash and then use it on the state's site to pay.