Proven method: Turn off your lights for 3 days, or only light the tank with blue light for 4-5 days (cyanobacteria do not absorb in the blue part of the spectrum). This is not long enough to harm corals, but the cyano will die off.
Reducing tank temperature to <74 F will also kill off most of it. I just noticed this in the last few months, when I gradually reduced my Q-tank from 80 to 73.5 F since the live stock were going to be transferred to a seahorse tank.
I highly doubt dosing nitrates will improve the situation. Nitrates are utilized by all algae, and the ones that grow the fastest will use it first... I would be afraid it could cause a hair algae bloom, or make the cyano worse.
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