NAF – New artifacts with unique properties.

Is it possible to make it so that a particular artifact appears on the map only in a single instance?

Yes, but only as a map generation setting. However, the problem of the same artifact appearing for sale will not disappear.

You can come up with workarounds, but it's not worth it (for example, prohibit the generation of artifacts higher than a major artifact for each map, but a special program will place them itself, etc.).