You can do this from the Pay Affiliates report. You can generate a Pay Affiliates report from the main menu under Affiliate Manager >> Pay Affiliates.

On the Pay Affiliates report, you can filter the report by a specific date range, using the date selectors. 

You can further filter the report by individual affiliates, using the "Affiliate" drop-down-- You can choose each one from the drop down individually and then view the result. You can also filter by other criteria-- minimum payout, minimum referrals.

As long as you are only viewing one at a time, when you mark it as paid it will only mark those who you are viewing (i.e. for that date range, etc.)

Once you've filtered down the report to just the affiliate(s) you want to generate a payment file for, or to mark as paid, you will find several options at the bottom of the Pay Affiliates page to execute those functions as described on the buttons. 

The "Mark as PAID" button is at the very bottom.