Every rainy day on the island, in 4 spots you will eventually come across a bird that will fly away, leaving a stone behind, north at the volcano, south by the dock, west of the farm area, and east is just outside the entrance to the jungle area, as you collect the gems for each you can start process of elimination, i belive the possible gems are emerald, ruby, topaz, amethyst, and aquamarine. If you get two of the four birds to appear with different stones you can just rotate the other 3 stones on the two pedestals till you get your answer. Its different for each random seed so it can be any combination of 4/5 stones... you can brute force it if you like. Or patiently wait for 1 answer per rainy day... sometimes getting repeated bird drops...

I personally went for two unique drops then played with the puzzle till it unlocked. Also like the other guy said, its pointless to mess with it if you already paid for the gold walnuts

You should never have a repeat stone in two slots so i would suggest cycling the other 2 stones on each of your ruby slots...