I'm thinking if this agent offered to let you make payments over time, he is padding things. The normal method is to make a deposit and a final payment.
It's typical that an agent will allow the passenger to pay the deposit, and then make as many payments as they want until final payment time. The agent just calls the credit card into the cruise line each time the passenger wants to make a payment. If the passenger is making payments with a check, the agent can send an agency check into the cruise line each time, although some agents will collect payments and just send final payment into the cruise line when it's due.
If there is a long time between deposit and final payment, this is a great way for passengers to pay down the balance and not be stuck with a very large balance due, all at the same time.