Maybe because your body can't inhale sufficient oxygen during your laughter, and is attempting to force oxygen into your body in shorter bursts, hence starting your body coughing, ie short inhale of breath between coughs? Just a thought! ☺
I was going to ask if you smoke too. If you have anything already around which could irritate like phlemgh (!?!?) or asthma issues when the extra air and movement of it (and anything else about in there) would, I'd have thought, cause an irritation (orrelfex to get air back out) causing you to cough.
I was a smoker but gave up for good about 16 months ago, I have suffered with bronchitas alot of my life, even as a child. I went to the doctor and he said I was OK when I was coughing up blood I had ruptured ? something but I have been OK since then. The coughing thing is relatively new though, but otherwise I am feeling fine.