The way I'd think about mapping them would be as follows...
Make a long plane in the front view. Divide it many times vertically, so you've got something like:
+------------ . . . --------+
| | | | | | | . . . | | | | |
| | | | | | | . . . | | | | |
+------------ . . . --------+
Then UV map it and apply the iris texture.
Next, bend the plane into a circle (no I'm not going to try and represent this as ASCII art
) and render it so that you get a good sized circular image map.
You can then apply this as a colour/bump map to the relevant area of your eyeballs using a straight planar mapping...