Coughing adjectives are listed in this post. Each word below can often be found in front of the noun coughing in the same sentence. This reference page can help answer the question what are some adjectives commonly used for describing COUGHING.
chronic, frequent
more, much
persistent, severe
violent
Hope this word list had the adjective used with coughing you were looking for. Additional describing words / adjectives that describe / adjectives of various nouns can be found in the other pages on this website.
a hacking cough