I had this type of problem in my home. However, it occured when the furnace turned ON.
In your case, it's possible that the RETURN duct is 'depressurizing' when the unit stops 'drawing air' from the return duct. The return duct is what 'feeds' the unit with air (in most cases), thus, it's 'shaping itself back to normal' at shutoff. To test this theory, what you can do the next time the unit turns on is go into the room where the unit resides, put your hands on the return duct where you think the banging is coming from, and feel if it's 'popping back into shape' when it turns off. If this is the case, either call a professional or talk to one explaining what's going on.
At the same time, this depressurization could be for a couple of reason (but not necessarily limited to them.) Some or all of your return ducts are blocked or obstructed (or accidentally 'plugged' with a coat by one of the kids), too small, or insufficient in number. So, it's not enough to 'fix' the banging with, say, extra bracing.
Other than that, others may have more to offer. My best to ya and hope this helps.