Combine black beans, corn, black-eyed peas, celery, red bell pepper, and green onion in a large bowl.
Whisk sugar, vinegar, oil, and black pepper together in a saucepan; bring to a boil until sugar is dissolved, about 5 minutes. Remove from heat and cool.
Pour cooled dressing over vegetable-bean mixture; stir to coat. Refrigerate for 8 hours or overnight. Drain excess liquid before serving.
