Carrots don't have sugar in, they are low GI.I offer him carrots and apple between every few days and a once a week, do you know of any veggies I can offer more regularly? I know Carrots and apples are high in sugar.
Just offer a variety of different fruits and vegetables each day. Dark green leafy vegetables like spinach or silverbeet, carrots (which you already feed him) apples, bananas, rockmelon, cucumber.
Don't feed him onion or onion relatives (garlic, spring onion, shallots, leeks) and no potatoe. Apart from that, just feed a little bit of fruit and veg each day.
If he hasn't been on green leafy vegetables for a while, only offer a small bit every couple of days and build it up over a few weeks otherwise he can get an upset stomach and have the runs.