what to say or do when the person next to you in a cafe always coughs?  

It is annoying. If someone were next to me in an internet cafe I would probably be unable to concentrate on my work! I might say, if you want to go get some water I will save your seat or like you said offer them a tissue. If they say they do not need a tissue tell them that they most certainly do because they are spreading germs. Even if we do not have a cold and we are coughing from a tickle or something it still spreads germs. I heard that even a yawn can spread germs.