We just returned from the Carnival Glory. The dining rooms each had one veg entree each night (2 one night). There was a pizzeria that had cheese, mediterranean, and mushroom options. The Asian booth had lots to choose from, but very limited hours.
The Red Sail restaurant usually had fresh fruit, but beware that the yogurt has gelatin in it.
If you tend towards whole grain foods, you may be a bit uncomfortable by the end of the 7 days as most items use white flour (pasta, breads, rice, etc.). A little box of Cheerios helped a bit.

If you are vegan, you may be out of luck--best to contact Carnival directly.