The greenest phones are the old-school, corded phones. I have one, but it's so hard for me to be tethered to the wall since I'm always multi-tasking. Phone calls double as dish-washing time or laundry time, etc. If you can't sit still while on the phone, there may be some hope that they're getting a littler greener.
I just got a new phone and check out the box. It's Energy Star compliant--standby power consumption reduction by 59% and says No RoHS-specified Chemical Substances used (meaning lead, cadmium, mercury, hexavalent chromium and specified brominated flame retardants). Looks like a step in the right direction. It also uses rechargeable AAA batteries. Go Panasonic!
By the way, the phone I chose is model KX-TG6412 if you care to check it out online. It's hard to find a phone without a built in answering system these days, but this is message free (they make the same phone with the answering system as well). The digits on the screen are extra large and easy to read, and I got a headset to go with it to minimize my EMF exposure.