My name is***** and I am sorry to hear that Max is coughing.
How frequently is he coughing? (once an hour, once a day, etc) Does he go to groomers, dog parks, or other places with lots of other dogs? Is he having any labored breathing? Any vomiting in the last few days? How is he eating? Does he have a fever (normal body temperature for a dog is 100.5 to 102.5).
My determination for coughing and if it is an emergency is as follows-
coughing more than once per hour
coughing waking him up from sleep
labored breathing or breathing with his head extended
unable to sleep because of coughing and/or labored breathing
If none of the above criteria fit with Max's current state of health, you can try giving him Benadryl. The dose is 1mg per pound of body weight, so he would likely take about 75mg. This is to treat him in case he has allergic airway coughing.
Does this help? Do you have any other questions?