Coughing captured in writing
Solution 1:
Cough is onomatopoeic. OED 1, s.v. Cough, v., recites Dutch and German cognates and remarks that “All these words appear to be of echoic origin, representing various sounds and actions made with the breath.”
Solution 2:
I would just simply use the word cough or maybe cough with an asterisk on each side. You could use ahem too but I think you would lose your readers, or at least make them think too much about a simple cough.