insulated means that it has a styrofoam box, inside the cardboard box.
Get a Bag, put plenty of water so that the coral is hopefully not exposed to open air (depending more on what you're sending). Tie the bag tight with an elastic and make sure there's a layer of air. Place the bag in the styrofoam cube or any type of enclosure, and try to ensure that it's not going to roll around, try and make it so that it's snug inside the cardboard box using more cardboard, styrofoam or whatever you got laying around. Put it in the box and away you go.
Depending on where you live, you might need a heatpack, or even wait til the weather gets cooler if you're somewhere hot.