Daphnia and rotifers are two small aquatic invertebrates that eat green water. If your fish are of a size that ignores daphnia, you can try them. Rotifers are vanishingly small. Just at the edge of human vision, the young are basically microscopic and the adults appear to be dots. They grow really well in and on sponge filters, so the long term permanent solution is to keep a sponge filter in the tank, but it will take its own good time to clear it up the first time.
UV filters are great for immediate results that don't add any chemicals to the tank water. They cost more than sponge filters to say the least, and the bulb has to be replaced about every six months, and the quartz sleeve much less often.