In skillet, melt 1 T. butter over medium heat. Add onion; cook, stirring occasionally, until starting to brown, 7-10 minutes. Add sugar, salt and Cajun seasoning. Reduce heat to medium-low; cook, stirring often, until onion is soft and golden brown, 5 minutes.
Meanwhile, bring large pot of salted water to boil. Add green beans; cook until tender, 4-5 minutes. Drain well, then add to onion with remaining 1 T. butter. Cook, stirring, until heated through, 1 minute.