I have a two year old son who weighs 26 lbs. He has a cough that keeps him from falling asleep. Is there cough medicine I could give him and how much?

Honey or codeine. We prefer not to give cough suppressants to children that young. Often a teaspoon of honey will soothe the throat so that the cough is better. If the cough occurs hours after the child is asleep and especially if it is so severe that it induces vomiting then I would be concerned about cough variant asthma and would have the child checked by your doctor.
Needs to be checked. He needs to be checked as cough may be from allergies or bronchial asthma. So consult his pediatrician to find the cause, before you give him any cough medication.