A pressure cleaner is by far the greenest way to clean a driveway. Other than that, the only thing I've really seen that works on black mold and mildew is the ZEP Mildew Stain Remover you can get at Home Depot. But it's the opposite of green. I doubt a pressure washer rental would be that expensive, especially if you only need it once a year. There are also power bars that you use like a broom; the water shoots out of holes in the end. Dunno if you can rent those as well, but it would be worth a call.
General Pump TriKleener Water Broom 14in. Width, 4000 PSI, Model# 2100306 | Pressure Washer Surface Cleaners| Northern Tool + Equipment