A few thoughts here that cover even the extremes in the world of coughing:
Quick fix is a cough suppressant. We've used several. Delsym is a 12-hour dose. You might have to ask your pediatrician for the right dose. Robitussin also makes one. I believe it's Robitussin DM that is a combo of a cough suppressant and guafinasen -- something that helps loosen congestion. Just read the labels or ask your doc. You don't want a combo of tons of meds. We typically get some sort of decongestant to help stop the post-nasal drip, and a cough suppressant. Your doc or nurse may tell you that decongestants may or may not work in kids as young as your son. They're right :) They worked for one of my kiddos, but did nothing for my other child.
Also, if this is new to him (meaning he doesn't suffer from this coughing year round), allergy meds aren't working, and keeps up for a couple weeks, I'd go back to the doc. It's quite possible that he could have a sinus infection even if he doesn't have a fever.
Lastly, the incessant night coughing sounds like many asthmatics I know, including my own son. If this is a chronic thing for him, you might ask some more questions at your docs office.
It can be hard to diagnose in kids under 3 though, and docs seem reluctant to diagnose, unless it's severe (i.e. sending you to the ER), before age 6. And unless the doc can "catch him in the act" his lungs may likely sound fine during an office exam -- which is during the day, when he's not having much of a problem.
I'd avoid Benadryl just in case because 1) as you mentioned, it's not working and 2) it actually makes asthmatic coughing worse.
You might try Zyrtec, but beware that it could cause mood changes. It worked for us, but made our son VERY disagreeable. He'd even disagree with himself! We suffered through it for a season though, then got a prescription for Singulair. Much, MUCH better allergy control, and no more grumpy/moody kid.