I have a large piece of old, dead and beautiful white coral in my 55 gallon aquarium. It covers about the middle 3rd of my aquarium floor, towards the back glass, up to within about six inches of the water surface. It doesn't quite fit into a 5 gallon bucket, width-wise. I had a lot of algae on it and had done all sorts of research on how to safely clean it, much of which was contradictory or onerous in terms of effort and time. Here is what absolutely works:
Entirely cover coral in a 9-1 mixture of hot water-bleach. No need to use more bleach, and less may even work (have not tried less). I use a clean, small kitchen trash can. You will see the algae disappear immediately. Leave coral in this solution for 10 minutes or so. Empty container and place coral aside while thoroughly rinsing the container with fresh water (until water emptied from container is clear). Thoroughly rinse coral with fresh HOT water (this helps dissolve any remaining bleach), then place back in container. Run a hose with fresh water into the container, filling it, and let the hose run slowly for about 30 minutes (I do this outside). Then, let coral soak for about 2 hours, rinse it with fresh water again, dry it and put it back in the aquarium. That's it. You may be able to cut the soaking time out - not sure - but even if you don't this is an easy process and can be done within a couple hours. No need to soak it over nite, or let it sit in the sun for days, etc., as I had read in many places. The same process works for rocks, plastic plants, and other ornaments, and in fact if there are not a lot of nooks and crannies like there are in coral, you can skip the soaking/hose running part entirely - just rinse the objects very well before putting them back in the aquarium. I do it that way with plastic plants and it works fine. Hope this helps alleviate any fear of using a small amount of bleach to make your aquarium ornaments and coral sparkle again!