I'm sorry that your question wasn't answered in a timely manner. Unfortunately, there's very little that owners can do for a coughing dog at home. Conservative care in the form of over the counter cough suppressants isn't recommended because none of the products have shown to be efficacious. A teaspoon of honey every couple of hours may be of value in soothing Dizzy's throat and reducing inflammation in that area.
The problem we face is that we don't know why Dizzy is coughing. At 10 years of age he may have contracted a simple respiratory infection just as any age dog can but 10 year olds are far more likely to suffer from advanced cardiopulmonary disorders which can cause coughing - congestive heart failure, heartworm disease, and chronic obstructive pulmonary disease (sterile bronchitis), e.g. - than much younger dogs and these disorders are treated very differently from each other.
Ideally, Dizzy should be thoroughly examined including careful auscultation of his heart and lungs before initiating any therapy. I understand your logistical constraints, however. In order to help determine the urgency with which Dizzy needs to be attended to, I need you to check his vitals...
1) Check his gum and tongue color. They should be nicely pink - not whitish (anemia) or bluish/greyish (cyanosis/hypoxia/lack of oxygen to his tissues).
2) Check his respiratory rate at rest. He should be taking less than 40 breaths/minute at rest.
3) Take his rectal temperature. Any body thermometer will do when placed 1.5" into his rectum for 1 minute. Normal is 100.5-102.5F. This is a two person job!
Please let me know what you find.