To keep them from turning green, I've heard to put them in cold water, just bring to a boil, then let them sit 15 min or so. Also to peel them, I had never done this until I think I saw it on the Food Network - after stopping the cooking in cold water, you can shake them around in the dry pan to get peeling more easily. Don't get too vigorous, LOL.
This applies more to egg salad, but for some reason I had never thought of crumbling eggs (you could do it with yolks for deviled eggs) with my hands rather than chopping them up. It is a real time saver and works just fine.
That's how I boil my eggs, too.
Start 'em in cold water to cover with a tiny amount of either salt or vinegar in it, then bring to a boil, put the lid on, turn off the fire and leave the pan on the burner for 20 minutes.
Take the pan to the sink and run cold water in it immediately and start rolling and cracking the shells all over, then peel them under running water.
Also, I make deviled eggs for get-togethers all the time and have to make sure I use "old" eggs that I bought at least a week or more before cooking.
Then they'll always peel perfectly and I won't have any rejects that can't be stuffed. There's more of an air space between the whites and the shell. I had a lot of friends *trained* to let me know in advance they were going to be wanting my deviling services a week or more in the future, lol.