Calculating Tray ceiling dimensions
It's pretty much up to you. Look at some pictures, find ones you like, make guesstimates.

When in doubt and looking for a ratio, there's always Phi (0.618) and 1/Phi (1.618) aka "the golden ratio" but you're still free to do with it what you will.

When you think you have an idea, grab some masking tape and mock up the outline on the ceiling (I'm assuming the ceiling is there, and flat, at the moment.) 

While it would be difficult to mock up the whole edge, you probably can suspend a sheet of cardboard at various heights (I assume you are lowering the edge, not raising the center, as that's more structurally simple) to get a feel for how various levels for the lowered edge feel to you, standing under them. If you find that a 7'6" ceiling height (18" down from 9 feet) feels too low, better it's a piece of cardboard you can easily relocate than the whole framing system and drywall.