There is a method for you to have zombie eyes,which is makeup.The following is my suggestion for you.
Firstly,you need to find a picture about a zombie.There are plenty of choices ,The vampire dairy,or The Twilight Saga ,The walking dead ,etc,choose the one you like,actually,I suggest you choose the picture based on the vampire dairy,of which those eyes are charming not ugly.
Secondly, prepare some eye shadow and eye liner,then draw your eyes with the same type of the picture you choose.
Thirdly,you may need to wear some special contact lenses to make your eyes color look like a real zombie.