Well, it seems that you would like to get a sun tan even if you have got pink eyes. But it would not be wise for you to expose your eyes to sunshine because patients with pink eyes are afraid of sunshine, some of them even develop watery eyes and photophobia. Anyway, sunshine has nothing to do with pink eyes patients anyway. So, you need to take some medicine and eye drops under the doctor's guidance and take care of your eyes from the point on.
Of course, you can stay in sun even if you get pink eyes. I don't know if the sunshine good for pink eyes. But i know that the sun will not impact the pink eyes. I was been told by my eye doctor when i suffer pink eyes. And i feel good when i stay in sun. So, just enjoy the sunshine yourself. Go ahead.
You should just stay in sun for a while which will help you get rid of the bacterium in the eyes. However, too much sun will irritate your eyes and make your pink eyes get serious. You could just drink more water to moisture your eyes. You should use the eye drops to release your pink eyes. The more vitamin C will make your eyes get moisture. The good sleep and diet will be so necessary.