1. Combine black-eyed peas, sweet onion, celery, bell pepper, and green onions in large bowl, and set aside.
2. Drain tomatoes, and place liquid in small saucepan with vinegar, oil, and Cajun seasoning. Coarsely chop tomatoes, and add to black-eyed-pea mixture. Bring tomato-juice-vinegar mixture to a boil, and pour over black-eyed-pea mixture. Stir to coat. Cool, then chill 1 hour. Season with salt and pepper, if desired.