Based on various orders recently appearing on the dockets, it appears that in-person civil jury trials will begin in May, under a centralized calendaring system. One typical order explains as follows:

The Southern District of New York has reconfigured courtrooms and other spaces in its courthouses to allow civil jury trials to proceed as safely as possible during the COVID-19 pandemic. Under the centralized calendaring system currently in place, the Clerk’s Office schedules up to three jury trials to begin on each day of jury selection: a primary case and up to two back-up cases that may proceed in its place if the primary case does not go forward.

Other examples of similar orders are here and here.