Not a naughty answer, but an intrigued one. Why should living at the seaside make a pet have a constant dry cough? I have had both cats and dogs and lived on the cliff top at Happisburgh (where the houses are falling into the sea) and none of my animals ever had a cough of any sort.
It depends more on whether you are there all day and whether you have the time to spend with a dog, if not then get a cat, but if you have the time a dog would love to live at the seaside. If you live near a busy road, then a cat is not a good idea. Also a cat would not appreciated being taken for a swim in the sea.