As for coral beauty, I just had one started to eat few days ago, after I purchased two days later. You try one of the follow, cyclop-eeze, mussles, or mysid shrimp, mine goes crazy for frozen mussles, but make sure its not too large.
Mine don't like frozen brine shrimp, they eat and spit it out, but they do eat live brine shrimp. BTW
, they seems to have a change of appetite quite easily, they just eat a few and would not eat any more, like you mention, they chase after the food and ignore it after getting close. Until the next meal time, they eat aggressively again. hee hee.