This was released this morning, the current episode order for most of the CW's shows for the Fall 2019-Spring 2020 season, including Supergirl and Batwoman. As of right now Supergirl's fifth season is slated to premiere sometime in October, alongside the rest of the Arrowverse(with the exception of Legends). As for Batwoman, it's been confirmed that it'll air on Sunday nights at 8 before Supergirl, which has been moved to 9. To round out the rest of the Arrowverse, Flash and Arrow will be airing on Tuesdays and Legends will likely take over Arrow's soon to be vacant spot after the winter hiatus. As for Black Lightning, it'll be airing on Mondays at 9.