“How can I stop my toddler's coughing?”

Consider getting your toddler tested for allergies. Nonseasonal allergies like dust and mold can occur before age 5 and a toddler and cause coughing. Alternatively you could try a over-the-counter allergy medication.

May have acid reflux. See pediatrician

The best way is to find out what is causing the cough and get rid of the cause. There could be dust or mold in the bedroom. There might be something he is eating that he is allergic to. Talk to your doctor and see if you can find the cause.

Coughing at the beginning of sleep and in the morning when waking usually is caused by inflammation of the sinuses (sinusitis). Coughing in the middle of the night is more consistent with asthma. A barky cough suggests croup or sometimes a cough that is left over from a viral upper respiratory infection. It is important to take your child to the doctor if they have a daily cough for longer than 4 weeks. You should also see the doctor if your child has a cough and another problem, such as: working hard with their breathing, or. breathing fast. 10 to 20 percent of preschoolers will cough for 3 weeks or more following a cold. Even children without a cold may cough on average 10 times a day but not consistently every day and usually not at night.

Good day! For the safety of your toddler the best is to visit a pediatrition. He/she will find the cause of the  coughing. 
Best regards,

It may be reflux. See your pediatrician or pediatric gastroenterologist. Good luck!