Coughs usually last from a few days to a few weeks depending on what is causing the coughing in the first place.
If you are just coughing do to breathing in things from the air or you have a cold that you're coughing along with then the cough will usually go away once the irritant or cold is gone.
If the cough lasts longer than 18 days then the cough could be caused by something more serious and I would advise going to urgent care or the doctor to get checked out just to be sure the coughing isn't caused by something bad.
Usually though coughs go away on their own or with some cough medicine within a few weeks at most.
The best position to sleep when you have a cough is to sleep with your head elevated by propping your head up on a pillow at least 4 to 5 inches.
When your head is elevated at least 4 to 5 inches gravity helps keep the mucus and post nasal drainage from getting into your throat and nose which helps stop the coughing.
I always sleep with my head elevated on a pillow when I have coughing and it does help a lot.
I would also recommend using a humidifier in your bedroom at night with some Vicks Vaporub as well to help get rid of the coughing.
Keeping moisture in your throat helps with the coughing and you can take a spoonful of honey at night before bed as well as during the day.
Drinking some warm tea with honey also helps lubricate your throat and moisturizes your throat as well and helps stop coughing at night and during the day.
I always keep a glass of water near my bed as well so if I do wake up coughing I can take a drink of water to help moisturize my throat and stay hydrated and then go back to sleep without getting out of bed.