In your checkout system, when the order comes through, make a call to the CreateInvoice API. This will generate the invoice in the PayPal system. You can use the "number" parameter in the CreateInvoice request to pass your regular order ID if you have one so that the invoices are nicely related to your checkout order.
Then, immediately after that call, make a call to MarkInvoiceAsPaid. This will mark the invoice as paid in the PayPal system so that you have a nice record of it there.
Sounds like what you're after, right?
If you happen to be working with PHP, my class library for PayPal will make all of the invoicing API calls very simple for you.