The Red Coris is a great fish if you prep your tank correctly. They are reef safe as they do not eat corals, but will eat shrimp, clams and crabs. But can damage corals by flipping the rock they are on as they search for food. And yes they are excellent at keeping bristleworms under control.
The solution to keep corals and a red coris happy in the same tank, is to properly attach them to large live rock too large to move. Rocks larger than a big coffee mug or heavier than 5 pounds are usually good, lighter ones are safe too if they are wedged tightly to a larger rock. I use epoxy putty and a Dremmel tool to attach coral frags.
A tool every reefer should have is also a dremmel drill tool usualy about 40-60 bucks. Make sure you use a carbide drill bit, and you can drill holes into your live rock easily that fit the shape of your frags. Then apply some epoxy putty around the frag and hole, it will dry and keep your corals extremely secure from being flipped.
For corals like frogspawn or torch corals, using black plastic click ties, loop around them and into a drilled hole to tighten securely.
Over time your corals will grow and fuse onto the rocks as well. If you have large areas of sand, you can also toss dead clam or snail shells and hide mysis or krill, like a wrasse toy treat.