As others have stated, Nothing is currently scheduled. May 4 was mentioned by some US airlines but with the SXM airport basically being closed (for 2 months as discussed the other day) who knows for sure.

And here was another "automated response" I got later on March 16.

Embassy of the United States of America

Bridgetown, BARBADOS

Thank you for your inquiry to the American Citizens Services Unit of the U.S. Embassy for Barbados and the Eastern Caribbean. Please note that this e-mail box is not monitored outside of business hours. If this is an emergency outside of business hours, call 246-227-4000 and ask for the Duty Officer.

If you are contacting us to report an emergency concerning an American Citizen, including a missing person, a victim of crime, a child abduction, an injury or illness, or a death of an American Citizen, please call the main Embassy switchboard at (246) 227-4000, where you will be connected to a Duty Officer who is on call 24 hours a day.