Is there a cure for hoarseness caused by a nodule on the vocal cords?

Yes: Vocal nodules are usually the result of voice misuse and abuse. Re-learning how to use your voice correctly with good vocal therapy and maintaining those good voicing behaviors is often curative for vocal nodules.

Yes: If the nodule causes hoarseness removing the nodule should help significantly. Most nodules form from trauma and it is possible that the nodule can go away if the trauma is stopped (much like a callous or blister going away by wearing shoes that fit). Prior to doing surgery a trial of speech therapy can be tried. If unsuccessful, surgery performed by an experienced ENT should be very helpful.