Try this.. overhead transparency film.. and rit dye.. hot water to nearly boiling. it's about .005" thick.
I'm pretty sure it will work.. so much so that i'm going to buy some black dye tonight because i have a tinting job i need as well.. from what i've read transparancy film is a different kind of plastic that can absorb the dye.. unlike lexan or something like that.
I'll find out for certain by the end of the weekend. It's kind of funny this thread popped up, because i've been waiting for the day to get over so i can get to the store and get some black rit dye for my project! (i already have the transparancy film..i use it a lot)