Here are some things to try.
The official answer If you get an error when trying to activate iMessage or FaceTime - Apple Support
The unofficial answer:
In order to get your time zone and time to update automatically, you need to have Location Services on. In iOS 8 it's under Settings, Privacy. Go to the bottom of the page where it says System Services, select that and make sure Setting Time Zone is on.
I suspect sometimes this still doesn't get the iPad to a time close enough to work, but it's a start. But we don't know.
Go somewhere to use another network, like the Apple Store. Try there. That way when you call Apple and tell them it's an AppleID problem they won't try to charge you or tell you it's a hardware problem.
Call AppleCare and insist on going up the tech support ladder. Second line or Senior Tech is as far as they'll send you, those guys talk to the engineers. Keep trying. I don't know if Apple really knows what's wrong either but this way they know you have a problem.
Go to imessage and Facetime sign in activation error iPad ios8.1.2 we started talking about this on page 18. Bookmark or follow to keep up with things people have tried.
Keep us updated and good luck