The first rental deposit payment is not due from the tenant until both the landlord and tenant have signed a rental agreement.
When the rental agreement has been concluded, the tenant has the right to pay their rental deposit over three monthly instalments (§ 551 Abs. 2 BGB). This is only in the case whereby the rental deposit equals three times the monthly cold rent. If the rental deposit equals two times the monthly cold rent, the tenant is allowed to pay it over two monthly instalments, and so on.
Remember, the landlord can never request a deposit greater than three times the agreed monthly cold rent.