I've been looking into this and I think it might be possible to do this. Ark Music Factory owns the publishing rights while Black owns the masters. Here are the emails to AMF:
Press and Media Inquiries:
Black's manager is Debra Baum of db Entertainment Group. Her email on her site is firstname.lastname@example.org
I don't know for sure who you would need to contact, Baum or AMF, depending on whether you'd need to get permission from whoever owns the publishing rights. You would need to get the masters from Black, I do know that.
What you can do: If you work with an authoring group you can see about getting a deal. If you don't work with a group you can show your support to them for getting the song released.