Contribution Status Updates, no more 'overdue'
Adding the contribution status itself is pretty easy. You can do that with Administer/System Settings/Option Groups, find the one for Contribution Status and click on 'options'. You will then get the possibility to add a value.

This is just adding a status, so I assume the settings of the status will be done manually. If you want to automate that you will have to develop a small extension that acts when a contribution is added or changed, and sets your status in relevant cases.

Am I making sense?