Unfortunately the word cough isn't an onomatopoeia, meaning it imitates or suggests noise of the sound -- like meow, roar or bang. This means that it is difficult to type the word as a noise in relaxed and colloquial phrasing, such as a letter or email. Therefore, writing the word "cough" is usually sufficient as everybody knows what it sounds like. However, if you must write out the noise then define the noise by breaking it down into syllables and then match up the letters.
Write cough in parenthesis, to use it as a sound.
Type it to represent sarcasm in written form for instance, "The pie you made was (cough) delightful (cough).
Write the word cough in a normal fluid sentence, for example, "Tim coughed as he choked on the pie."