Zoanthids -- unlike palythoa -- feed on the very tiniest of zooplankton. CE is too big for most of them. Target feeding with a very fine slurry of chopped food (with the pumps off) is the most promising method. This slurry can certainly include CE; it's a great food. Oyster eggs are a more appropriate size, but too expensive for routine use.
If you have palythoa, they can take somewhat larger pieces and will be more aggressive about feeding, but generally you don't need to do much at all with these guys; they are very good at growing with no help at all.
There is no need at all to buy expensive bottles of "coral food" which are mostly water. Making your own from the various saltwater foods available in fish stores plus human grade seafood is easy, much cheaper and has no preservatives and chemicals and freezes well for ease of daily use. Just be sure to include as wide of a variety of foods as you can. This is where your local Asian market is your friend: the range of seafoods available in a well stocked Asian market is astonishing. (And often quite creepy to those with western notions about seafood.)
Your carnivorous fish will be happy to eat it, too. Just make a batch with larger chunks for them.
Depending on the species of LPS, many feed by absorption. They will react to target feeding, but won't actually eat it. LPS with distinct polyps (like blastos and acans) target feed easily.