I, too, think a chile or carnation would not be a good idea. Both require significant laminar flow for food collection, and historically live less than say 6 months in most tanks. This is not only just my opinion, but a rather accepted premise in this hobby. They are like gonioporas- while some have success, the vast majority just die in captivity.
As family mentioned, there are many LPS that can do very well in indirect light though. Many of the really fleshy LPS (ie- scolymia, lobophyllia, trachyphyllia,etc) can do quite well in situation such as this. Sun corals quite simply just require constant feeding. No other real specialized requirements, so if you are willing to feed every day or two SPECIFICALLY to this coral, go for it, but if not, dont get one.