We Have the same problem here in UK when there has been too little sun or the area that is getting the green slime is a very shaded area when there is a lot of dampness like a water run off drain or such.
Most people use a MOSS killer that you can mix in the watering can and spread it on the slime area but it will return again IF the damp problem is not fixed.
My way of dealing with it is to mix a watering can with hot water and add a tea cup of vinegar to the can, mix and spread on the green area, you may find you have to repeat this a few times to get rid of the green but it's better than chemicals as far as I'm concerned.
The other method is household Bleach that some folks use for whitening their clothes, about the same amount of bleach as there was given for vinegar but the
bleach should work faster, be careful with the bleach as you need to make sure you dont get it on other stuff as you go and dont pour against the lawn edges or onto flower beds.
After the Vinegar has done the job, I give the gravel a good rake over so the Moss don't get to spread and every few months give another rake to prevent the greenery forming. As before, try find out the cause and make sure you keep the cure up or you will always have the same problem.
Good Luck, WeeNel.
AND DO NOT MIX the bleach and vinegar under any circumstances- causes chlorine gas that is toxic. VINEGAR is actually best to use because it kills the organisms responsible for the green, bleach can just whiten without removing them (vinegar carries the sediment away with it),