I've heard others who use carrots and peas as treats. But, I read somewhere that they don't actually digest it well so you may see the entire piece come back out in the poop.
I say...if your pup can take it without any effects, go for it. But if he gets gas etc, you can consider something else
For treats, my little ones eat Merrick's Lamb Lung fillets! They love it! And I love it because it doesn't get messy
I usually break them into tiny pieces, the size of my pinky nail. I realize they don't care how big the piece is, but rather how many times they get a treat lol