Cool mist vaporizer or steam humidifier (depending on whether cool mist or warm steam sounds more pleasant).

And/or go to the doctor and get a scrip for codeine. That's the only thing that knocks out Ed's persistent unproductive coughs. (Well, they also gave him an inhaler, which also seems to help.) I don't think it much matters what triggered it originally (virus vs. allergy) -- coughs are like any other irritation, they can become cyclical and self-perpetuating until something breaks the cycle.