What would you suggest i do to cure a babys cough without medicine?

Nasal suction: If an infants cough is related to nasal mucus and post nasal drip, one can use a small amount of nasal saline drops in the nostril followed by bulb suctioning to remove the mucus. If the cough doesn't improve or is associated with rapid breathing, wheezing, stridor (high pitch) then its wise to see your pediatrician for evaluation and specific treatment.