How in the world would you propose to 'get them to stop'? Do you think they are coughing voluntarily outside your window and just asking them politely to please refrain is in any way reasonable?
I have a chronic cough, and I *HAVE* seen a doctor. I know it's hard for other people to listen to, but it's not like I can just switch it off.
I have to breathe. Coughing makes it possible.
Sometimes you just have to put up with stuff.
My old boss had asthma, and at times her coughing was very loud and she'd cough all day long. Her office was right next to mine and I could clearly hear every single cough. It was annoying and, frankly, sometimes the sound was unpleasant to listen to.
She was under medical treatment. In fact, her doctor was sending her to specialists to see if there was any way of relieving some of her symptoms. Asking her to stop coughing would have done nothing--she was coughing because she had to.
In any shared living situation, like apartments, there will be noises that bother us. My downstairs neighbors stay out late at night and frequently the closing of their car doors under my window at 2 am will wake me up. But they aren't slamming the doors shut, so there's nothing anyone can do about the noise.
I see the coughing as a similar noise. It's there and it's annoying and sometimes bothersome, but it is not a voluntary noise that can be controlled to any great extent. It's not loud music, it's not stomping on the floor, it's not slamming doors.