First off, there is no such thing as organic or truly green nail polish; any brand that claims as such is blatantly "greenwashing."
That said there are cleaned up formulations available to those looking for an alternative to the – frankly toxic – mainstream brands. There are the 5-free formulas (notably sans formaldehyde and by products like formaldehyde-resin), and there are the water based formulas, which are basically water and acrylic polymers. I wouldn't recommend the latter for little ones who habitually suck their thumbs, or to anyone who washes their hair vigously and regularly, or does the dishes without gloves. Water based polishes deteriorate rapidly under warm, wet conditions.
Scotch Naturals and Aquarella are the leaders of the pack when it comes to water based polishes, and in my experience, Aquarella is the better of the two. I'm not wild about having to repaint my hands every other day, but it holds up nicely for pedicures.
And these two sheer shades below layer beautifully for a glossy water color stain that reminds me of summer popsicles.