Saruman's ring, to be honest I doubt it ever existed. Saruman may have told Gandalf that he had a ring to frighten him... after all, the ring was never seen, (actually I must check this as I haven’t read that bit for a while). However, on the other hand, Saruman's desire for the ruling ring may have drove him to make one for himself, after all he, like Sauron, is a Mara. Therefore, it is not beyond possibility that the Madness of the ring drove him to make his own. Yet his ring was never seen, so how do we know if it ever existed. As Gandalf said one of Saruman's greatest weapons is his lying tong.
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