I can think of a few options, but to me they all sound awkward. It's hard to say if it's idiomatic, because I don't have enough experience to know it. Those options are "tell him he's a good boy", "pat the dog", "give the dog a sweet", but all of them are a bit awkward sounding. Is there any better option?
"Reward your dog" is correct and clear, but perhaps not specific enough. If you want to describe a particular method of rewarding your dog then mention exactly that.
Often rewards are "treats" (small meaty snacks that dogs love) So you could specifically say "give your god a treat"