No, emerald dragons are not breedable with any dragon. This is true of all of the birthstone dragons.
I was trying to get the emerald dragon by breeding a crystal dragon with a linge dragon. But i got a  dragon
Another dragon
Another dragon
You don't breed a Kairos Dragon in DragonVale. You have to get parts to complete it.
The emerald dragon is one of the limited edition birthstone dragons. It was only available during May of 2012. The egg was emerald green. It took 31 hours to incubate, and another 31 hours to hatch. It was bred with a crystal dragon on the left and a lichen dragon on the right.
you breed a ice dragon with a mine dragon
You have to breed a plant and a fire dragon.
As of July 2012, there has not been a star dragon in DragonVale.
You have to either buy it for 500,000 gold, or breed water dragon with another water dragon.
You have to breed a sun and moon dragon together
You have to breed a metal and a water dragon together.
You have to breed a plasma dragon with a salamander dragon.