Mix black-eyed peas, coconut milk, corn, tomato paste, curry powder, sugar, and 3/4 teaspoon salt in a pot until smooth and evenly combined; simmer over medium-low heat, stirring often, until curry sauce is heated through, about 5 minutes.
Pour enough water into a separate pot to almost fill and bring to a boil; season with a pinch of salt. Add rice to boiling water and cook, stirring occasionally, until rice is very soft, about 15 minutes. Drain excess water from rice.
Mix rice and curry sauce together in a large bowl.
