How can I get rid of this smoker's cough without actually quitting smoking?!

I just quit, wish me luck...and I have barely coughed since.

You aren't going to get rid of it until you give up smoking. In fact if you continue to smoke it will grow increasingly worse. When you get a cold it will affect your chest and lungs more and more until you can't breathe properly. I should also mention the wheezing you are going to experience whenever you breathe. Quitting is a healthier choice and can be done if you put a lot of effort into doing so. Sometimes being a quitter is a good thing.

Former smoker--approaching my 9 year anniversary of going cold turkey.