Personally, I think they can damage your eyes to some extent. You know how tanning beds work, right? They try to imitate the sun to give you the effects that sunlight brings to you, making you as if you are enjoying a sunbath. Well, on the other hand, it also means what you get is not only just comfortable feeling but also uv rays. Yeah, damn right, harmful uv rays! It will cause damage to your skin and your eyes at the same time.
Yes, tanning beds with naked eyes is bad for the eyes. But it won't cause blind in most of cases. Commonly, your eyes will exposed in the sun when you tanning. The intensive light and UV rays in the sun are really bad for the eyes. It is said that long time exposed in the sun will contribute to cataracts. Apart from the UV rays, long time stay in the sun with naked eyes also cause to sunburn of the cornea because of the heat in the sun. If you suffered from it, you will experience increased tear production, pain, and swollen eyelids. So, if you want to tanning outsides, you'd better prepare a pair of sunglasses to shield the eyes.