In a medium bowl, whisk the yogurt with the lemon juice, lime juice, ginger, garlic, hot paprika, coriander, cumin, turmeric, chopped cilantro, 2 teaspoons of salt and 1 tablespoon of oil.
Transfer the marinade to a very large resealable plastic bag and add the quail.
Seal the bag, pressing out the air, and turn to coat.
Refrigerate the quail for at least 8 hours or overnight.
Remove the quail from the marinade and let stand at room temperature for 30 minutes.
Light a grill and oil the grates.
Lightly season the quail with salt and pepper and grill over moderately high heat, turning once, until the breast meat is barely pink, 8 to 10 minutes.
Transfer the quail to a platter, garnish with cilantro leaves and serve.