[Boromir88]

One possibility is Saruman actually never made his own ring, but found one of the lesser rings and attempted to use it. He most likely would have continued to study the ring in a further attempt to make his own. Whether Saruman made a ring, or found one, it is clear that the result was like one of the "lesser rings."

In an earlier draft of Gandalf's discussion with Frodo in The Shire, there seems to be more evidence Saruman made the ring he wore:

"There was much talk of rings at the White Council...even wizards have much to learn as long as they live, however long that may be. There are many sorts of ring, of course. Some are no more than toys (though dangerous to my mind) and not difficult to contrive if you go for such things - they are not in my line."~HOME VII The Treason of Isengard: The Fourth Phase (1)

To Gandalf these lesser rings are "toys" and "trifles," but still dangerous to him. It is not in Gandalf's mind to make a lesser ring, but it wouldn't be difficult for a wizard to craft one, if he had the mind for it. And one thing that is continually stressed in Saruman's fall is that he had long delved into the studying the works of Sauron, especially Ring-lore.

However, this is not in the final text, and I think in the final versions, the evidence that Saruman crafted his Ring gets even slimmer. All that's mentioned is Gandalf suspected Saruman was close to the secrets of their making, but no confirmation that he had succeeded. In fact, it appears there were still some "missing links" in Saruman's study of ring-making:

Saruman, failing to get possession of the Ring, would in the confusion and treacheries of the time have found in Mordor the missing links in his own researches into Ring-lore, and before long he would have made a Great Ring of his own with which to challenge the self-styled Ruler of Middle-earth~Foreward

Now this is Tolkien explaining how his story is not allegorical to WW2, however, I think it still holds some important info about the character of Saruman. That is, there were missing links into his studies of ring-lore, he would have only found in Mordor. Being a "wizard" and always able to learn, he would have found the keys to ring-making, but it seems like he was still missing this pertinent info in LOTR.

It is only Saruman, who in a boast declares:

For I am Saruman, the Wise, Saruman Ring-maker, Saruman of Many Colors!"~The Council of Elrond

Capitilization of "Ring-maker" is interesting here, because it suggests a title or name. Saruman is not an occupational "ring-maker" he is "Ring-maker!" All the more interesting, considering it is the same name Gandalf gives to Sauron:

"Behind that there was something else at work, beyond any design of the Ring-maker."~The Shadow of the Past

So, in Saruman's trapping of Gandalf, his boast "Ring-maker" sounds more like Saruman trying to fashion himself in the style of Sauron, not that he was actually a "ring-maker." Although, that really just comes down to interpretation. Personally, I think Saruman found one of the lesser rings and tried to study it in hopes of furthering his study into ring-lore and their making. I think the othe interpretation would be Saruman was successful in crafting his own Ring (as would be possible for wizards who had the inclination for it), but this would have been a "toy" and "trifle" of a lesser ring.