after lunch or dinner, depending on how desperate he seems, I give lucca a big carrot. The first time he wasn't so sure about it, but now he LOVES them. They're straight from the fridge, so they're nice and cold. I started giving them to him for the same issue: he was always hungry after meals (even though he gets about 5 and 3/4 cups in 3 sittings), but I dont want him to get fat -he's already on the large side....
Anyways, yes.... Try carrots. I assure you he'll love them, and you'll have to start giving some to Kira too cuz she'll want them too... Or you could try mixing in some green beans with his food... Good luck!