If your dog is coughing, check his mouth for a foreign object look down his throat to see if you see anything. If the coughing continues, but the dog has no fever and still has an good appetite. You can give a cough syrup to help with the cough.
If the cough is dry harsh and persists, get in touch with your dog's veterinarian. It maybe Kennel cough which is a highly contagious respiratory infection.