My dad is currently going through radiation treatment due to oral cancer and has mouth sores and throat irritation. What meds are good for dry cough?

Saliva aids... Ask his doctor(s) or dentist to prescribe pilocarpine lozenges or lollipops if appropriate, try to find Xylimelts at local pharmacy, products from PerioSciencres will be very beneficial. As a last resort get sugar free lemon drop hard candies. I prefer the other options first.