Finally returning to this since I am soon to have that Fin Fun tail I've been dreaming of. So after a bit of research on my own, here is what I have found.
A lot of people recommend Jacquard paints for fabric. Looking at their site, this seems like it could be a good idea since their textile color line promises to keep fabrics soft, can be thinned with water to increase transparency and reduce viscosity, and work well on synthetic materials. The only down side is the heat setting, which could be troublesome.
Since I've altered my plan a little to include wanting a blue gradient for the upper half of my Aussie green tail-to-be, I've tried to find methods for that. Most suggest dyeing the fabric, but apparently lycra and spandex don't handle being dyed well. RIT claims their dyes can do it, but I am skeptical, and I really do not want to mess this up. Maybe I could just dip it in really, really diluted fabric paint? Has anyone tried anything like that?
Anyway, here is a promising gradient tutorial I found:
http://craftthyme.com/how-to-ombre-dye-fabric/