PS2 black console does not communicate with controllers

Sounds like you have wireless Controllers. Be sure your batteries are good on the Controller and the controller is turned on, LED should light. Plug the receiver into the controller jack, and it should light up at least one LED. If you have channel number selector, set it to the same number on the controllers, channel selector.

If old wired controllers will work, then you have dud wireless controllers. I know that cheap poor quality wireless controllers exist out there. You may have a dud. I also know that sometimessomething kills the controller ports on the PS2. The only way to know is to hook a wired controller you know works into the port to see if the port is good or bad.