What are the nitrates, in both the tank and the source water? Phosphates? Silica? Lighting (type, wattage, and time)? What type of plants? Sounds mostly like diatoms--does it peel off easily? With live plants already in there, I'd guess there's an imbalance in nutrients or light--meaning more nutrients than the light will support the plants into using, or else a shortage in a specific nutrient the plants need to really grow well, or third, that you have slow growing, low light plants that won't be able to outcompete the diatoms. In any case, adding more fish won't be the solution.
I understand that you are not adding more fish, but with livebearers, you either have to remove the fry to another tank, or add something that will consume the fry to avoid overstocking.