what about using those no flame candles? they even have them that change colors to add drama??? Just a thought

Thanks, but a) I have no idea what those are, b) I'd like something that can be turned on whenever I like and stay on (til I turn it/them off). Somehow the idea of candles (unless I'm wrong about those) sounds very impermanent and that it might end up being 'flickery', which I'm not really interested in.

If you use one light you will get a bright spot no matter what. depending on how you make it-rope lighting is a good bet or led light bars set into the edges under the piece. You also need to have a good bright white reflective surface to evenly diffuse the light back up into the stained glass. Do a google search for "light box" these are used by glassers to cut glass. your table will have to incorporate this general idea to do what you want it to. Good luck!

Thanks - I discovered light boxes today and will look into them (not cheap!), thanks again. I also might do something with mirrors.

I've made glass block lights with stained glass on the outside and christmas lights on the inside and the light looks pretty even to me. Also, they are a cheap/easy thing to experiment with first.

Yes I was going to say christmas lights either the small ones or the large ones. Also you will need some kind of support for the glass or it will sag in the middle depending on how big it is. You could build or buy a shadow box put the stained glass on top & lights inside. i have seen tables like this where you can put things inside to show.
Good luck.