If you have set up Private Payer Categories, you can filter by category on the Manage Invoices page by clicking the blue "more filters" hyperlink to the left of the 'Search' box at the top.
There will now be a new dropdown called "All Private Payer Categories" where you will be able to select your Private Payer Categories to only display private invoices whose Payer is linked to the selected Category. Click the green "Go" button in the top right to generate your report.