The manufacturer's setup instructions for some wireless printers specify that you should press a "WPS button" on your Wi-Fi router. There is no such button on AirPort devices, but you can still use WPS (W-Fi Protected Setup) to connect a printer, provided you're running AirPort Utility 6.2 or later.
If AirPort Utility is outdated, run Software Update or download the latest updater from the Apple Support website. Then follow the instructions in this support article under the heading
Method 3: Associate the printer to your Wi-Fi network via WPS
To see that part of the page, you must first click the disclosure triangle next to the heading
Adding a Wi-Fi printer that does not let you select a Wi-Fi network via the printer's built-in controls or screen