While cycling, it's important to monitor ammonia, nitrite, and nitrate levels. Otherwise, it's hard to say when the cycling period has run its course.
If you're setting up a reef tank, you'll also want to test your alkalinity, calcium, and phosphate levels (at minimum -- many other tests available), with testing for magnesium being useful from time to time (but not so important if you keep up with water changes and have a light to moderate number of corals).
I've never had the water itself turn green while cycling, but that indicates that there's a free floating / swimming form of algae taking off in your tank. Depending on how green your water is, it could be a battle to get rid of it if it doesn't clear up on its own as the cycle wraps up.
Are you running your lights while you cycle?
If so, they really aren't needed, as there shouldn't be anything in your tank that requires any light while the tank is cycling. Cycling without the lights helps to reduce the amount of nuissance algae that grows while cycling. Your post makes it sound like there's corals in your tank... I hope not while cycling, as the stress of the ammonia and nitrite spikes will likely damage them extensively (if it doesn't kill them). Or, do you mean there's dead corals in there (coral skeletons turning into live rock)?