Yep, you're definitely over-cooking the eggs. I consistently had this
problem too, until I got this amazing little gadget from Brookstone. It's
an egg timer. You place the egg-shaped timer in with your eggs and cover
them with cold water. Boil the water and the egg timer changes color to let
you know when the eggs are soft-boiled, medium or hard.

If I keep my eye on the timer, the eggs come out perfectly every time - no
green rings!

I did a quick search and found a link for this item on Cooking.com...
http://www.cooking.com/products/shprodde.asp?SKU=103760

I've had my egg timer for about 12 years and it's still going strong!

Good luck!

Kilikini