There are types of corals that are non-photosythetic, they get all or most of their nutrients from feedings not light.
look for sun coral, carnation coral, A lot of the gorgonians, goniopora (this do not do very well in captivity). Like I said I am still not sure if this would work well, as these corals do need frequent feedings, but I am not sure if they would do well in a "dirty" (high nitrates, phosphate) environment.