This is Dr. Christian. Welcome to JustAnswer. Honey isn't toxic to dogs. In large amounts it might cause vomiting or diarrhea but otherwise shouldn't cause any problems. Are you wondering if you can use it for the cough?
The only way a cough like this could be caused by something he ate is if it was trapped in his throat. If he is calming down that is unlikely. The more likely cause is an infection. The best options to night are to keep him calm and perhaps even put a humdifier in the room where he sleeps tonight. If the cough is still present by morning then have him seen by your vet. If things worsen tonight then don't hesitate to have him seen at an emergency clinic.