Your pharmacist will know, essentially you are looking for something that does not have an anti-cholinergic effect which is what causes the dryness.

there are different cough medicines - ones that promote coughing by thinning the congestion making it easier to cough up and and ones that act to stop the cough all together. I personally go for the ones that help me cough during the day and ones that stop me coughing during the night. Can I remember which ones have the anti-cholinergic effect? Nup. But if I had to guess, I would think the ones that thin the mucous and help you cough would be least likely to give you dry mouth. Could have it completely round the wrong way though....