As Laura has said, white or colourless stones are appropriate. Pearls have certainly become de rigueur, especially among royal ladies. I am guessing that most of them have a plethora of wonderful pearl necklaces, earrings and bracelets, and while diamonds are technically "colourless" stones, it is the setting that denotes how appropriate they are.
I think one of the royal necklaces best suited to mourning is Camilla's three-string necklace with a diamond clasp is a perfect balance. The pearls are the most beautiful colour and the diamond clasp can be worn at the back under her hair for daywear and exposed for eveningwear.
https://s-media-cache-ak0.pinimg.com/736x/90/fc/9e/90fc9e981dedd619f373459bd27555b4.jpg
I think this is the choker that Mathilde wore to Pope Benedict's funeral. Please correct me as the photo isn't quite clear to I tried to find another photo to show the choker.
https://4.bp.blogspot.com/-E-kS5Otz...woKpSgCLcBGAs/s1600/MATHILDE+pearl+choker.jpg