What is the best medicine to give a 6 month old who is coughing?

None: Plenty of fluids to keep the mucus loose, watch for fever, or decrease in drinking or eating or a change in behavior. If cough persists see your doctor. Over the counter cough and cold remedies are over-marketed and do very little real good, & can make kids cranky or too sleepy & even prolong a viral illness. Avoid them. Only exception is if the cough is due to allergies, then plain benadryl (diphenhydramine) ok