A coughing dog visiting a dog park may be a dog park danger, if he is infected with the bacteria causing kennel cough or the virus causing canine influenza. (amcny.org)
This may mean delaying going to a boarding / daycare facility and not visiting dog parks or taking walks around the neighborhood. (texvetpets.org)
So wait till after your puppy has all his shots before visiting the dog park! (petsmagazine.com.sg)