How to light a tray ceiling?

I do not recommend the rope lighting. As the individual lights burn out it looks awful and you have to replace the entire length. It also yellows. If you have lots of room fluorescant strip lights will work. They would be the least expensive way to go unless you purchase the dimmable type. Another great type of lighting for that situation is miniature track lighting with small quartz lights that plug on to the track. These would be dimmable. Go to any specialty lighting store and take a look at it.

Hope your project goes well.

Ron