Greek myth containing a ring?

Is it the ring of Polykrates you are thinking about? It's a legend more than a myth.

The story goes that Polykrates, the ruler of Samos, is visited by a friend, and he boasts about his luck. The friend warns him repeatedly not to annoy the gods, as every bad news that is coming in is balanced by one of luck and success, until Polykrates, to placate the gods, throws his most valuable possession, a ring, into the sea. A few hours later the cook brings the ring back to him, he had found it in a fish he had bought. The friend leaves quickly, in order not to be caught in the upheaval he is sure to be imminent.

Inevitably fortune turns against Polykrates, he is captured by the Persians and crucified.

Between the world of the living and that of the dead there are, it is said, great rivers and dread streams. First, greatest and outermost is Oceanus, which winds about the earth and the sea with nine rings, but is also a subterranean river. The river Styx (river of Hate), which is a primordial figure too (daughter of Oceanus), is a branch of Oceanus and a tenth part of his water is allotted to her. So Styx, which flows out from a rock, is the tenth ring, though some say that Styx itself corrals the souls in the Underworld with nine rings.

in one myth zeus gives a sirl a saphire ring that belongs to hara.hara puts some kind of curse or something on her and then the godess of love helps the girl.

The reference is from Plato-- the story of a ring that rendered its wearer invisible.

atlantis was in the shape of rings with the same center

Do you mean Sigfried and the Rhine daughters?