First, all health articles say persistent coughs should not be taken casually but got properly checked up as it can be a symptom of something more serious, for e.g. tuberculosis or even cancer (as we very recently found to our great sorrow). So do get it checked up. Please.
In my mother’s case it was due to the fact that, with increasing age and other problems, she spent almost the entire time lying down, getting up only for her meals. This caused the phlegm to accumulate and no amount of cough syrups or other medication helped on a sustained basis. This had been going on for a few years, and she used to cough and cough and cough.
I gave her tulsi (holy basil) in her morning and evening tea. I got a small pot for my window sill and would pluck a few leaves each day, then wash them well and boil them for a few (say 5) minutes in water. Then made tea, in the usual manner with this water – the leaves would be strained out alongwith the tea leaves. An improvement was visible in a few days and with regular use the cough reduced to next to negligible.
(The above photographs of tulsi have been downloaded by me from the Net, if I have violated any copyright, please let me know and I shall remove them immediately)