Stir together turmeric, pepper, and 1/2 teaspoon salt in a small dish. Sprinkle fish with spice mixture.
Heat 1 tablespoon oil in a large nonstick skillet over medium. Add half of fillets; cook until golden and fish flakes easily, 2 to 3 minutes per side. Remove from skillet; keep warm. Repeat with remaining 1 tablespoon oil and remaining fillets.
Wipe skillet clean with paper towels. Add rice, coconut milk, sugar, and remaining 1/2 teaspoon salt to skillet; bring to a simmer over high. Cook, stirring often, until thickened, 3 to 4 minutes. Stir in 1/4 cup cilantro and lime juice. Divide rice mixture among 4 plates. Top evenly with carrots and fish. Sprinkle with coconut and remaining 1/4 cup cilantro.