Theoretically, tomato juice would be OK on the diet. It would better to make your own rather than trust to the freshness of the bottled stuff. I wouldn't drink tomato juice too much when you're following the diet or you could become intolerant to it.
You could mix it into chicken broth (I would make your own for the same reason stated above). If it's only chicken than there's no risk of becoming intolerant to it.
Alternatively, just put it in water, close your eyes and think of getting better.
When you have Sugar cravings, have some protein or vitamin C. That should help you.