What an interesting idea!! I think it would look great.
So, how to do it. My first thought would be to build a 'tray' ceiling. This would be angular but perhaps easier. Just drywall a recessed box. You may want to make a plywood box and install that and drywall over it.
As for a dome recess - These guys may be able to help you
RWM-inc. Crown Mouldings and Radius Mouldings- archway moulding, window moulding, door moulding
You would build a circular recess (easier said than done) and then put a radius cove inside the recess.
What a great project - I want to see some pictures when its done.