Using a tutorial I found by Krishnamurti Martins Costa, I modelled the eyes to have two layers, an inner layer where the iris was flat and the pupil indented, and an outer layer that would form the shape of the lens, and provide a reflective and wet look.
Then, using the image below, I created an eye texture with a blue iris. I wanted the eyes to stand out from her red hair and costume, and also added a yellow centre, as I liked the idea of having multiple colours.
These are the final colour map I used:
Once the texture was applied to the eyeball model, I selected only the white parts of the eye, and applied a subsurface scattering to achieve a realistic look.
On the outer layer, I applied a mental ray mia_material_x and changed the settings so that the inner layer would show through, but the reflectivity would give the eye a realistic wet look.