There must be an evolutionary reason why the rest of our bodies have melatonin – why not eyes? By design they are fairly exposed to the rays of the sun.
I’m sure I’ve read somewhere that the retina actually regulates the amount of melatonin (and therefore melanin, which gives us our tan) produced based on the UV rays it detects. Melanin diffuses UV rays and thus a surface tan protects deeper cells against the sun’s harmful rays. If the eyes tanned it would potentially reduce the amount of UV rays that reach the retina and therefore mean less melatonin/melanin produced, resulting in more damage due to UV rays. Over however many million years the eye has been evolving, the creatures with tanned eyes died of cancer and so didn’t spread their eye-tanning genes.
Disclaimer – I’ve not studied any form of genetics/evolution/physiology for about 13 years, so the above may be utter guff.