Your leather coral does no need to be fed.
Your brain (please specify what type - Trachyphyllia, Favia, etc.), Euphyllia and Bubble Coral can be fed small bits of meaty foods. Mysis shrimp works very well. Pretty much anything you would feed to your fish that's small enough to fit into it's "mouth".
Acropora and Montipora need very small food. I think you're generally looking for things in the 200-600 micron range (that's a very rough guess on my part). Things like rotifers, baby brine shrimp (possibly), oyster eggs, and a host of commercially prepared coral foods (like DT's Golden Pearls or Rod's Food) can be used.
As Lobster alluded to, your corals (especially SPS) are usually eating various types of plankton naturally in your tank (zooplankton, baterioplankton, etc.) whether you realize it or not.