Well, the best thing to do is to increase the frequency of water changes that you've been doing. I'm curious about which kind of protein skimmer you're using on the tank. Also, is there a refugium going in your sump? You note your nitrates read zero, but you don't mention your phosphate readings. If you don't test for those, you ought to and if they are elevated, even marginally, get yourself a couple of reactors for a tank of the size of yours and run a good phosphate reducing medium, like Rowaphos, through them. You might want to run them all the time, even when there is no cyano-infestation.
I wouldn't normally suggest this for a new tank, but if you increase the amount of water changes, your skimmer's working well and it's adequate for the amount of water in your system, you are growing Chaeto or some other macro-algae in your sump, etc. then get a product called Chemiclean, which is specifically for the purpose of killing cyano and use it strictly according to instructions. This will not address the cause of your cyano-problem, but it will, at least, slow it down temparily and stop it from effecting your coral, if you have any.
But, even if you do try the Chemiclean, you should continue to try to address the cause of the cyano and prevent it from getting what it needs to proliferate in your reef.
Don't get discouraged...You'll figure it out and resolve the problem so you can enjoy your tank.