Amethysts and turquoises are quite a rare combination, and a modern one (i.e. mostly from not earlier as the mid-20th century). The colours of these stones are in sharp contrast, and therefore can be considered as clashing colours. Besides, amethysts are translucid stones, whereas turquoises are opaque stones, which makes the match between these stones quite audacious.
Among royal jewels, the only amethyst and turquoise jewel I can remember of is the Duchess of Windsor's Cartier necklace, acquired by the Duke of Windsor in 1947:
The sketch of the necklace by Cartier:
The Duchess of Windsor wearing the necklace at a reception in Paris in 1953:
At another reception in Palm Beach, in 1957:
There was a matching bracelet, also made by Cartier, but purchased by the Duke of Windsor only in 1954. It is worn by the Duchess on the picture immediately above. It has been bought back by Cartier.
According to this site : http://www.telegraph.co.uk/luxury/jewellery/cartier-tradition-to-sell-the-duchess-of-windsors-bracelet/ "The bold colour scheme [of the bracelet] was nothing new for the Duchess – she already had a décolletage-spanning bib necklace in the same stones created as a special order for her by the maison in 1947, awash with the violet and sky-blue stones in twisted gold and interspersed with diamonds. The Duke had commissioned the piece, supplying his own diamonds and amethysts, but was thankfully convinced by the formidable Jeanne Toussaint that the necklace would benefit from the addition of dozens of turquoise cabochons. The purchase of the bracelet just a week before Christmas in 1954 must have seemed a trifle by comparison."
Regarding Queen Ioanna/Giovanna of Bulgaria, I am sceptical about her necklace containing turquoises. It looks like amethysts and pearls for me. But if someone could provide a coloured picture, I would be gladly corrected!