I don’t know how old he is, but would any of these work?
gargling with warm salt water (recommended by pediatrician)
lozenges, or even sucking on hard candy (I’ve heard marshmallows are also good, but I don’t like marshmallows, so haven’t tried them myself)
spray cough medicine that I think just acts locally
Vick’s plug-ins or patches
Warm beverages - chicken soup/broth, my mom used to make me jello - but I liked drinking the “jello water” before it gelled, these days I like Bigelow’s I Love Lemon tea with honey (you could use another sweetener, or do without, but I don’t know if it would be as good for coughs)
popsicles
My kids used to like eating the frozen strawberries in sugar syrup (thawed)
I remember my great-grandmother talking about how they used to boil onions to make cough medicine, but we just used OTC products, so again, I’m not sure how effective it would be