This is the eye I used for a fan-art of Mike from Monster University. It includes the iris texture, and you can replace the sky texture to an HDRi to have more interesting reflections and lighting.
The materials are fully procedural. Shapekeys are used to change the size and shape of iris, and size of pupil.
*** EEVEE COMPATIBLE ! As of the 26th of November, this eye is now fully compatible with eevee thanks to the devs ! You have to enable screenspace reflections and tick the refraction box in render settings, and to enable the screenspace refraction for the "cornea-sclera blended" material.
It is in CC-0, so you don't need to give me credit but it would be nice to send me a link of what you did with it :-)