There are several ways to approach a cough (have a look in the Respiratory System module)
Nerve calming herbs like wild cherry bark and mullein
Antispasmodics like gumweed and cramp bark
Michelle is right that getting a diagnosis and ruling out bad stuff for chronic issues is a really good idea too.
Anti-histamines like Brigham tea or nettles.
Then of course there are the expectorants like elecampane, gumweed etc…
Don't use herbs or combine herbs with medications or use them during lactation or pregnancy without talking with your healthcare provider.