The Dragon Breeding Nest

Originally, you may only breed one Draggy, but after 10 6-hour periods, you unlock the ability to obtain a Furious Dragon. After another 10 6-hour periods, you get the chance to unlock the Lightning Draggy. After yet another 10 6-hour periods, you may get the Stormy Dragon. Then, you can get a Green Draggy after another 10 6-hour periods, and a Sayan Dragon after another 10 6-hour periods.

Each period is free. It can be sped up to the next period with the use of 3 cash for a Draggy, and 15 cash for a Dragon.