If you can find Jamaican curry powder, use it and omit the allspice. If not, use regular curry powder and add the allspice to it. Add 6 tbsp of curry powder, more if you like it more spicy.
Cut the meat into large chunks, maybe 2-3 inches across. Feel free to add the bones if you have them; you can remove them later.
Heat the oil in a large pot over medium-high heat. Mix in 2 tablespoons of the curry powder and heat until fragrant.
Pat the meat dry and brown well in the curried oil. Do this in batches and don’t overcrowd the pot. It may take a while to do this, maybe 30 minutes or so. Set the browned meat aside in a bowl. (When all the meat is browned, if you have bones, add them and brown them, too.).
Add the onions and pepper to the pot and sauté, stirring from time to time, until the onions just start to brown, about 5 minutes. Sprinkle some salt over them as they cook. Add the ginger and garlic, mix well and sauté for another 1-2 minutes.
Put the meat (and bones, if using) back into the pot, along with any juices left in the bowl. Mix well. Pour in the coconut milk and tomatoes and 4-5 tablespoons of the curry powder. Add 4 cups of water. Stir to combine. Add the thyme.
If you want to cook on the stove, bring to a simmer and let it cook until the meat is falling-apart tender, which will take at least 2 hours. Longer if you have a mature goat. If you want to cook in a crockpot, transfer the mixture to the crockpot and cook on low for 8-10 hours.
If you have cooked the meat on the stove, add the potatoes when the meat is close to being done - tender but not falling apart. Cook about 30 minutes or until the potatoes are done. Then, skim the fat off the top of the pot if needed.
If you cooked the meat in the crockpot, boil the potatoes until tender. Skim the layer of fat off the top of the curry, if needed, and mix in the potatoes.
If you used bones, remove them before serving.