Are you positive that carrots are out or do you just say so from the standard diet.
I cannot have fruits, but I can have carrots and apple (because they're not so sweet).
A bunch of Celery with 1/2 apple is fantastic for candia (without the apple the taste is very bad). I personnally have one carrot juice a day, 3 on a bad day and it helps me a lot: to assimilate easily the essential vitamins they contain and to keep drinking a lot of liquid so as to help my body in its cleansing process.
Did you try a search online? I am afraid that these are my two famous juice recipes!
Beet juice is also fantastic, although like carrot it is a
bit sweet (and very good for the liver, both carrot and beets).