Carrots aren't all that good for them. Too high in sugar and it can mess with their gut flora and fauna. Broadleaf weeds of the right type are the best diet.
Here are a bunch of suggestions:
Mulberry leaves
Grape vine leaves
Hibiscus leaves
African hibiscus leaves
Blue hibiscus leaves
Rose of Sharon leaves
Rose leaves
Geraniums
Gazanias
Lavatera
Pansies
Petunias
Hostas
Honeysuckle
Cape honeysuckle
Leaves and blooms from any squash plant, like pumpkin, cucumber, summer squash, etc...
Young spineless opuntia cactus pads