The launching of a barge usually brings a splash of cheer. But as the Jeffboat shipyard in Jeffersonville, Ind., dispatched barge No. 6402 last week, a touch of sadness hung by the Ohio River across from Louisville. The occasion marked the waning of the era of riverboat building, if not its end. Jeffboat, Inc., once launched up to 15 barges a week. This barge, a grain vessel, was the last. The inland waterway fleet is overbuilt and underused, and Jeffboat, its work force reduced to 70 from a 1981 peak of 2,300, will retreat into the repair business. Jeffboat folds up what Manager John Briley of the Ohio River Museum in Marietta calls ''the last major shipyard'' on a river that once boasted one in almost every town.