I've found mullein to be really helpful for some persistent coughs that I get after cold-weather cycling. It's an herb that you prepare similar to tea - put a heaping spoonful of it into a bag or a teaball (with enough room for the herb to expand), pour boiling water over it, and then cover it with a tight lid and let it steep for a half an hour. (if it tastes bad, add cinnamon and honey).
Mullein is a gentle herb that supports lung functioning - you can find it in any of those earth-toned food stores that sell bulk herbs. if they don't stock it, they can order it for you.
If your coughing bothers your throat, pick up some Slippery Elm tablets. SE is a demulcent, which means that it supports mucous membranes - that stuff feels really good on the throat.