they feed on phytoplankton but they have VERY low survival rates regardless of how you feed them. They appearently need a constant supply of phytoplankton to the point where its impossible to keep reasonable water quality.
edit: what scientific species do you have, I could be talking about something different. or at least what color is it and when you say shrinks and expands do you mean closes up? I ask because sometimes carnations are called christmas tree corals but there is also another nonsymbiotic coral commonly called christmas tree coral (which I have and is relatively easy to keep. it does open and close several times a day and is normal).