By coral, I am assuming you mean bleched, dead coral skelletons?
If so, typically, some algae on the coral skelletons is desirable. It gives your tank a more natural appearance, it adds to the food source [to a small degree] for your vegetarian-loving fish like tangs and angels, etc.
If, however, you want a continuously no-algae setup, then roll up your sleves, cause you will be constantly cleaning rock. Your best bet is to allow some algae to accumulate, but before it gets out of hand, remove your coral and give them a good scrubbing with a tooth brush [deadicated] unter warm water to get the algae off. Of course, coral being porus, you are not going to get all of it off, some will stick in the pores, etc.
If you can't stand algae and must get it off, then you can do one of 2 things or both. First, you can let the sun do the job for you. Removing corals and letting them bake in full sun will kill off much of the algae. This is the SAFEST way to achieve what you want. If you want it totally clean, then your rocks will have to be soaked in a solution of bleech and water. For this you can use a big plastic trash can, or individual buckets. For buckets, a cup of bleech mixed in with water will do, letting your coral heads soak. An hour ought to do it. Following this, again, the saftest thing to do [if there is a safe way to deal with bleech in this hobby] is to rinse, rinse, rinse, and when you think you've rinsed enough, know that you haven't so rinse some more. Then leave the coral in the open sun all day, turning them.
You must get rid of the bleech or you will kill everything in your tank. The sun breaks down bleech fast. Following the rinse and sun, if you really want to play it safe, replace your corals in fresh water, use a fresh water declorinator then let sit for an hour. Test the water using a fresh water declorination kit. If you get zero readings for clorine, take a deep breath then add the coral back to your tank. [Try adding one or 2 small pieces at a time and watch your fish closely for a couple of hrs for any sign of stress related to clorine posioning before adding in the rest of the cleaned coral].
Anything short of the above procedure reduces your chances for not adding toxin to your system.
I have been an aquarist for over 20 yrs, and I have had total wipeouts in my aquarium 2x's due to bleech poisoning [and not being careful enough]. Since the last time, I swore off bleech cleaning. Healthy green and red algae can be a beautiful and beneficial additon to your tank. The brown stuff, if that's what bugging you, is harmless and it will go away once your tank ages.
Good luck!
