Customers enter their own price/donation

Please help:

I am need to create a "payment center" site with zen cart. This is the senario. It is for a timeshare resort who charges their customers once a year for their room. The customer gets an invoice from the resort. They have a couple months to pay the fees. What I need to know is if there is a template/module/whatever where the customer can go on and pay whatever amount they like. This will be done with a secure third party credit card company. No paypal (I wish this wasnt so, but not my choice).

For example:

I have a $200 bill for my room. I go online to the website to pay. But, I only want to pay $125. So I enter $125, checkout and get a recipt.

Is this possible? Please note to book keeping will be required from the site. The office will handle each transaction accordingly. Please help.

This is most certainly possible, but I personally don't know of any plugins which have this feature.

Most likely this is something that's going to have to be coded from scratch.