I have successfully dyed maple rings that were 1/8 thick. I used powdered rit dye mixed with denatured alcohol. I put it all in a mason jar and put a vacuum pump on it. I cycled the vacuum on and off every 30 seconds about 6 times and let them sit for a few hours. They float until you vacuum them, then they sink. I took them out of the dye and hung them up to dry over night. The color goes all the way through.
Don't let the rings sit in the alcohol for too long or they will change shape.