Although Sony never manufactured first-party wireless controllers for its PlayStation 2 console, there are plenty of third party accessory manufacturers that have made fully compatible wireless controllers. If you are having trouble with one of these controllers, it might be initially disheartening to learn that Sony can offer no official support. However, many of these issues are quite fixable.
The most common problem with wireless controllers for the PlayStation 2 is a lost charge. Because the PlayStation 2 hardware does not support USB charging (like modern consoles) batteries must be used to keep the controllers powered on. Even if the wireless controller turns on, but does not respond correctly to inputs, the batteries may still be the problem. Try changing the batteries, and then turning the controller on again to see if this helps the problem.
If it has been a long time since you used your PlayStation 2 wireless controllers, or you have recently used them with a different console, then they might not be synced with your console anymore. If the controllers have a sync button (generally located on the flip side of the controller or between the analogues) try pressing this button and re-syncing with the receivers. If your controller does not have a sync button, try turning off the controller and then turning it back on to re-initiate a new sync.
If all else fails, attempt a full system restart. Unplug the wireless receivers from the front of the PlayStation 2, turn the controllers off, and then turn the system off. Make sure the receivers have not gathered excess dust, and then plug them back into the PlayStation 2 and then turn it on. Finally, power on your controller again and then follow the correct procedure to re-sync it with the console. If the controller still does not work, you may have a defective product and should contact the manufacturer if the product is still in warranty.