Option 1: I think having a separate Payments database with a calendar view would be a way to do it and do a relational db between Payments and Clients database. From there, you can just call the page "PAID" for every entry on a calendar view. You can even just create a filter like "Name starts with...PAID" and so whenever you create a "New" page within that database, it automatically fills the name of the page as PAID.

Option 2: Another simpler method would be to have a "Payment Date" property for the clients. Then create a Calendar view and call it Payments and just drag the client's name to the date for when they paid for the month. With this method, you can just keep track of when they last paid so you lose the historical tracking of payments, however.