Solder

The solder will definitely soften to the point of liquidity before the rest of the coin, and then you could use something like a solder sucker - a spring-loaded plunger-type tool where the plunger springs backward, creating a suction which slurps the solder off the surface - to pull it off. However, a residue will almost certainly be left which will forever identify the coin as ex-jewelry.

There are chemical processes which will do it. All of them will seriously damage the coin.

Some jewelers have this skill, and they can be counted on to be aware of the value of your coin.

Putting it on and taking it off are two entirely different skills.

Whether or not the ring can be safely detached depends entirely on the person that originally did the attaching. What kind of solder did they use, and how was the surface of the coin prepared for soldering? The answers to these questions will determine whether or not your job is going to be simple, or impossible.

Jewellery solder is different from electronics solder. The most important thing a jeweller is aiming for is structural integrity - that the two objects will remain connected and the join will not move, bend or break when stressed. Ordinary electrical solder is a very weak metal and not very suitable for this purpose. But stronger solder requires a higher melting point; an ordinary soldering iron might not even be hot enough to move it.

You might find that the jewellery solder used is in fact very close to the composition of the coin itself. In which case, removing it without damaging the coin will be impossible, since the melting points will be too close together.

It's also possible your quest is doomed from the start, because the jeweller physically damaged the coin by filing, drilling, smoothing or scraping the edge to allow for a better soldering surface.

I don't hold out too much hope for you. Making coin jewellery without damaging the numismatic value of the coin is hard work, and most jewellers in the past didn't bother; they were mainly interested in making beautiful jewellery and didn't give a hoot about the numismatic value of the coins they played around with.

There is a braided copper wick(ChemWick in Canada) which is flux coated specifically designed to soak up solder. Place the wick over the solder and heat the wick with the iron. The coin will get very hot regardless of what method you use, but you can put as much of the coin as you can in a damp paper towel as a heat sink and clamp. There will be a patch of solder plated area left behind. If this is just on the edge of the coin, you be golden.

The mechanical de-solder devices will no doubt leave you with a hot flying coin with molten metal bits thrown in for good measure. Learn how to use one as intended before getting all experimental with it. As for the type of solder used, the higher melt point that should have been used will definitely be near impossible without a proper wattage iron and more possible damage. If lower melt alloy you may get really good results with the wick. I use this stuff professionally, and if you rub the hot wick over a flat copper pad on a pcb(as intended use) ALL the solder will indeed be lifted if you keep on feeding through clean wick. The abrasion of rubbing and the clean wick results in a copper pad surface that is... MS69 red.

... but work can be such an inconvenience

Basically what Sap said is the main thing. There are numerous types of Solder, many types of flux, differences in temperature on preparation. As an example there are many types of Silve Solder for jewlery purposes and if using a Silver sensitive type of flux, the actual metals to be connected are fused together. I've used this for making permanent rings on women's Silver bracelets for the charms. Once used it is permanent. Of course there are Lead free Solders, Aluminum Solders and many, many others.
Unfortunately if you heat most solders they will run over the surfaces of the coins they are on. Running of Solder is the one really nice thing during the Sodering of Copper water piping where you heat the pipe and the solder RUNS into all cracks and crevices.
For the Silver coin the chances of someone using Silver Solder is fairly good and if so, to late. The surface of the coin has been blended to the material.
Yes this is a pessimistic outlook but if those coins were made into something by the average jewler, not much could be done to make the coin back to the way it was originally.
Might be worth it to experiment though if the coins are worth the trouble.

I have a lot of experience with solder, but none with removing solder from coins.

I would try solder wick first, again, I have never tried to remove solder from coins. An easy touch and application a little at a time is the way to go. Good luck.

The problem still is that the coin would probably be ruined as a coin from even the best solder removal. But not much to loose trying though.