Which of the two bank accounts (current or savings) is more suitable for depositing rent, or should both be avoided due to dealing with a usurious bank?

It is not permissible to deposit money in interest-based (riba-based) banks unless there is a necessity and no Islamic alternative exists. This should be limited to a current account, not a savings account, as it represents the lesser of two evils, from the perspective of cooperating in sin rather than directly engaging in riba. The Fiqh Academy and religious scholars have issued fatwas prohibiting dealings with interest-based banks when an Islamic alternative is available. They have permitted deposits out of necessity, provided no interest is taken. The rent can be given directly to the homeowner or via checks, or deposited into her current account if necessary.