The shit cough occurs in only one situation: When a person is shitting in a public toilet with only one cubical and numerous urinals. This leads to embarrassment at the sounds emitting from the bowels of the shitter and they then cough to muffle the sound of the "plop" or the "squelch". This is especially evident in those suffering of diarrhoea.
"I was in a McDonalds in London coz i needed a shit right? But the urinal was surrounded. I tried waiting on the sounds from the hand-dryers to muffle the sound of my shit but no cunt was using it so i had to blast out a shit cough. I think the other guys at the urinals still knew I had the runs though."