Are you making black tea kombucha with no problems?
Are you using any of your black tea kombucha for starting the green tea? If not you will need to use white vinegar to keep the PH down to prevent decay, mold etc. Try to use at least 10 percent kombucha (preferred) or vinegar to start your batch. That should be enough to prevent decay. You can also try rinsing your jars with white vinegar right before you start a batch. That should kill any stray bacteria that got into the jar at the last minute.
By the way, it is perfectly ok to use black tea komubcha as a starter for green tea kombucha.