I'm assuming you mean Fisher? If so, then I agree with the 1236-X2. Besides, it can also be used for other things, as it is quite a powerful detector.
First, remember that any detector will find rings - they are easy, in fact, being single loop inductors.
Other jewelry may or may not be so easy. Fine worked gold and filligree, small chidlrens rings and so on are harder to detect. What is needed is a detector that has an affiinity for these. That normally means a higher operating frequency than common coin detectors. It also helps to accept that such gold falls low on the conductivity scale so low discrimination should be used. And these sorts of jewelry items tend to give poor responses, meaning you have to be willing to dig even iffy items that are at foil discriminate and above.
I tend to go with the detector that gives the sharpest response to iffy targets in this case, and that is also the 1236-X2 in your price range. If a Fisher isnt a requisite, then I would suggest one of the Tesoro's. Also the Garrett Ace 250 fills the bill well.
Finally, here are two truisms you may not hear when we start arguing detectors:
1. It's not so much the detector, as where you take it.
That means you gotta take it where the odds are high that rings can be found. Even the highest priced model will fail if you don't do that.
2. Gold jewelry looks like junk to a detector
That is a fact of life. If you are really serious about finding jewelry, get a detector with notch and eliminate everything above and below the midrange. If you avoid diggin' foil, pulltabs, or screwcaps by whatever means, then you can pretty much give up on finding much gold jewelry. The rule of thumb in jewelry hunting is - if it signals at foil or above, recover it.