Eyes are parts of the head NIF, and share the same texture, so there's no need to do anything in CS.
You basically need to edit the texture in a graphic editing program, like GIMP or Photoshop. Both will need additional plugins to edit .dds textures.
First, you'll need to find the specific texture. Easiest way is to browse head meshes in NifSkope. You'll find the texture name and path in the window on the left of the model itself (the window is toggleable with F2 key).
When you find that texture, you can start editing it to your likings. When you finish, there are basically two was to proceed:
1) Have the change affect all head of this type. Just save over the .dds file.
2) Make new head with changed eye color. You'll need to save the texture with a new name. Then, open the head NIF and change the texture to the new one, and then save as a new NIF file (not overwriting the old one). Lastly, you'll need to add the head head in the CS.
-Open Construction Set and load mains master .esms.
-Go to Body Part tab
-Right click somewhere and select "New"
-In the new window, specify - ID (identificator), Part (set as Head), Part Type (set as Skin), Female (select if it's a female head), Playable (select so player can select it in character creation), Add Art File (select the newly created NIF file), Race (obvious) and Type (Normal or Vampire). Then just save as new .esp file.