The good news, at least the good hope for fans of the show is that it may migrate over to the NBC/Universal owned cable outlet The Syfy Channel for new episodes with a new name - “Hellblazer” and with the same actors attached.
According to showrunner Daniel Cerone in a recent statement to fans, “NBC made some early pickups but ‘Constantine’ not canceled. We’ll pitch them our plans for 2nd season in May. Then they decide. Anyone putting money in studio coffers by purchasing ‘Constantine’ in any form will motivate studio to find a home for show. The more international viewers the better. Foreign sales can drive a series. Keep it on air. Look at 'Hannibal' for proof.”
I have to agree with Grizzly’s sentiment that the show would probably find a more amenable audience and likely more breathing room to develop the show further within the cable franchise than on network television. Syfy and “Constantine” (or “Hellblazer”) would be a good fit.