Do you mean strictly green or blue, or are you interested in colors like olive and chocolate?
Easter Eggers typically lay green or light blue eggs. They are available pretty much everywhere and sold falsely as Ameraucanas, Americanas, or Araucanas. About 70% will lay green or blue and the other 30% may lay shades of brown, white, tinted, or pink.
Ameraucanas lay blue eggs. You may be sold birds as Ameraucanas but unless you go specifically to an Ameraucana breeder who sells true Ameraucanas, you are most likely recieving Easter Eggers.
Araucanas are one of the ancestor breeds of Ameraucanas. They also lay blue eggs, and similarly, in their true form only come from a breeder. A real Araucana will have ear tufts (not ear muffs) and be rumpless.
Cream Legbars lay sky blue eggs but are considered a rare breed and can be difficult to find.
Welsummers lay a dark, coppery brown egg, as do Barnevelders. Hatchery birds will lay lighter eggs than breeder birds.
Marans lay a dark, chocolate colored egg. Some breeder stock may even produce near black at times, but even hatchery stock should produce a decently dark egg. The Black Copper variety lays darker eggs than the other varieties. The breed can be hard to come by.
The Penedesenca lays an egg similar to that of a Marans. They are quite rare but an enjoyable addition to a flock.
The Olive Egger is generally a cross between a blue egg layer and a dark egg layer. Some may come from multiple generations of breeding rather than a simple first gen cross. They are often bred at home by hobbyists but some large hatcheries have acquired Olive Egger stock.