Why is my puppy sleeping more with a smelly green discharge?

The two most likely possibilities here are that Vada has a primary infection relating to her urogenital region, or that Vada has a puppy vaginitis. If it is the former, systemic antibiotics will likely be required to clear things up. If the latter is the case, puppy vaginitis can unfortunately be a very frustrating situation to deal with. It is usually unresponsive to antibiotics, and the best thing you can do is try to keep the area clean with some antibacterial wipes and probiotic wipes. The green discharge will likely continue to come back but hopefully in lesser quantity, thickness, and odor. Some of the research into this area is suggesting that the best way to help with this condition is to spay Vada AFTER her first heat cycle instead of beforehand. This would be a matter to discuss with your veterinarian after you and he have determined whether or not this is the condition that Vada currently has.