They'd probably want to get it out before Corocoro. Paul Ryan is acting like he's seen more then Zeraora
Others are saying the date will be between 9-20th of April

While Corocoro could just have nothing and they could do a Direct anytime, but if we go off the basis of Corocoro revealing anything , I think it's coming on the 6th. Typically they fall on Fridays, and Corocoro usually leaks around the 10-13th, 13th is also a Friday, but Gamefreak and TPCi have been trying to get beat Corocoro leaks recently

It's happening on the 6th