There are a few things you can do. None of them matter until you fix your nutrient issue. Until then the cyano will just be replaced with something else if you eradicate it. It is good to get things when they are small.
You can not water change your way out of cyano. It can double itself every 20 minutes. The only way to beat it with water changes would be 50% water changes every 19 minutes. It's an insanely resistant organism. It's survived for hundreds millions of years, and large extinction events. Don't be to discouraged it's surviving in your tank.
Personally, with cyano I always seem to find it in lower flow tanks. Not because cyano can't hold on in higher flow, but because lower flow tanks have more dead spots so food/waste can rot. If you increase the flow, and randomize it so there are no dead spots, this really helps with removing the nutrients before the cyano or algaes can become a problem.
The second very common thing is if you used dry dead rock for it to be leaching nutrients and phosphates back into the water. If this is the case I find that higher flow, in combination with more aggressive skimming, daily filter sock changes, and a daily low dose of lathium chloride works well. (two little fishies lathium chloride is great and this is the intended purpose)
If you have resolved the water movement issue, your nutrient issue is solved, it is time to attack the cyano. If you have a small tank and are not keeping acro's then I'd try a 50% or so water change, turn the tank lights off for a full 72 hours, and wrap the tank in a sheet or blanket so it gets NO light. The cyano will die. If you wrap it for 71 hours, or if you turn the lights on to feed, then the strongest cyano cells will live, and you will make your problem worse. 72 hours really is a magic number. Do another large water change after the 72 hours.
This can be problematic if you are keeping SPS and your pH drops down.
