In book 6, Harry Potter and the Half-Blood Prince, in Chapter 4, when Dumbledore takes Harry to meet Slughorn, he is using Gaunt's ring to attract Slughorn:
He shrugged and spread his hands wide, as though to say that age had its compensations, and Harry noticed a ring on his uninjured hand that he had never seen Dumbledore wear before: It was large, rather clumsily made of what looked like gold, and was set with a heavy black stone that had cracked down the middle.
Than later on in Chapter 10, after seeing Odgan's memory, the ring is still in Dumbledore's office:
He turned away again, and was almost at the door when he saw it. Sitting on one of the little spindle-legged tables that supported so many frail-looking silver instruments, was an ugly gold ring set with a large, cracked, black stone.
Then, at the end of Chapter 13, after Dumbledore's memory with young Tom Riddle, comes this:
Harry got to his feet. As he walked across the room, his eyes fell I upon the little table on which Marvolo Gaunt's ring had rested last time, but the ring was no longer there. "Yes, Harry?" said Dumbledore, for Harry had come to a halt. "The ring's gone," said Harry, looking around. "But I thought you might have the mouth organ or something."
So we see that the ring was destroyed somewhere in-between - that is, in the middle of Harry's 6th year.
But in the 7th book, Harry Potter and the Deathly Hallows, in Chapter 33 "The Prince's Tale", we learn that:
And now Harry stood in the headmaster’s office yet again. It was nighttime, and Dumbledore sagged sideways in the thronelike chair behind the desk, apparently semiconscious. His right hand dangled over the side, blackened and burned. Snape was muttering incantations, pointing his wand at the wrist of the hand, while with his left hand he tipped a goblet full of thick golden potion down Dumbledore’s throat. After a moment or two, Dumbledore’s eyelids fluttered and opened.
“Why,” said Snape, without preamble, “why did you put on that ring? It carries a curse, surely you realized that. Why even touch it?”
Marvolo Gaunt’s ring lay on the desk before Dumbledore. It was cracked; the sword of Gryffindor lay beside it.
So the ring is destroyed in the same night Dumbledore found it!
Can someone solve the conflict?!