There is a product made for the purpose called 'Wet & Forget'. I bought it on special somewhere but have not used it yet. Al

Fix the sprinklers to prevent it and cut back the ivy. My guess is most of the water is being reflected back out onto cement.
Bleach will kill it also...temporairly.

Gee, and I try to propagate the stuff on purpose. I even painted some of my broken concrete to make it look mossy.

You can spray a ferrous sulfate solution to kill moss and algae.

We get that every winter during the rainy season,then when it gets nice,warm and sunny it bleaches it out,so I don't worry about it anymore,just let nature take it's course.
Easy peasy.
Kathi