Soak the kidney beans overnight (or for at least 8 hours) in water. Drain and rinse before using.
In a large pot, combine the kidney beans, rice, coconut milk, water, garlic, thyme, allspice, and salt.
Bring the mixture to a boil, then reduce the heat to low and cover the pot.
Simmer for 30-40 minutes, or until the rice is cooked and the liquid is absorbed.
Remove the pot from the heat and let it sit, covered, for 5 minutes.
Fluff the rice with a fork, remove the thyme sprigs, and serve hot.