Does anyone know if you can smoke on the balcony of your cabin on a cruise ship.

i don't think there is a general rule of thumb, so you should ask them that question.

bon voyage...

http://www.cruisemapper.com/wiki/676-smoking-on-cruise-ships
I have been on many cruises, but my wife gets seasick, so I have a travel buddy with whom we have sailed and traveled often.
The last time we cruised, we were able to smoke cigarettes and cigars on the open deck, but not from our balcony. My buddy and I only smoked cigars. It was a good place to meet other passengers.
I forgot which cruise line, but there was a Churchill smoke room on one of the ships where I shared a Cuban cigar with another passenger. It was a Partagas D4, my favorite. He was from the midwest. I think he was in second heaven. LOL

It is allowed