I'm sorry to hear that your fellow seems to cough after yawning, lying on his back too long or when vocalizing, which hydroxyzine has not improved.
Dogs rarely cough in response to allergies, so I'm not surprised hydroxyzine didn't help, although it won't hurt him either so it was worth trying.
A cough simply means he is experiencing airway irritation.
A cough can be related to heart disease, including heartworm, lung disease secondary to a viral, bacterial, fungal or parasitic infection or tracheal irritation due to a bacterial, viral or fungal infection.
But sometimes a cough can be related to post-nasal drip, or gastroesophageal reflux.
If he has any signs of dental or gum disease a thorough cleaning may help.
As some dogs age their gastroesophageal sphincter weakens and stomach acid may reflux up into the esophagus or pharynx leading to a burning sensation which can cause a cough. Reflux is more likely to happen when the pup is laying down (especially on their back), or with a big yawn. As time goes on the stomach acid can cause some laryngeal burns/irritation too which can cause a cough.
In case this is related to acid reflux there are medications that you can purchase over the counter that may help by reducing stomach acid. You can give either:
1) Pepcid ac (famotidine) at a dose of one 10mg tablet per 20 to 40 pounds of body weight every 12 hours
2) Prilosec (omeprazole) at a dose of one 20mg tablet per 40 to 80 pounds of body weight every 24 hours
These are acid reducers which should help decrease stomach acid production and thus decrease the burn with reflux and decrease coughing. They are quite safe and can be used long term if necessary.
Some older dogs also have problems with laryngeal function and paralysis or polyps as they age.
These can be diagnosed via your veterinarian giving light sedation and observing laryngeal function and looking for polyps.
Best of luck with your fellow, please let me know if you have any further questions.