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Voldemort opened the Chamber of Secrets when he was at school, and wrote it all down in his diary. Since that same diary was used as a Horcrux, it seemed to have come with a set of instructions on how to use it to bring Voldemort back. So why did the Death Eaters wait until Harry was in his second year, something like 12 years, to bring him back with the Diary?

Dumbledore explains this to Harry in Chapter Twenty-Three of Half-Blood Prince. Voldemort only gave the diary to Lucius Malfoy, not to any other Death Eaters, and he didn’t divulge anything about it being a Horcrux:

“Well, it worked as a Horcrux is supposed to work — in other words, the fragment of soul concealed inside it was kept safe and had undoubtedly played its part in preventing the death of its owner. But there could be no doubt that Riddle really wanted that diary read, wanted the piece of his soul to inhabit or possess somebody else, so that Slytherin’s monster would be unleashed again.”

“Well, he didn’t want his hard work to be wasted,” said Harry. “He wanted people to know he was Slytherin’s heir, because he couldn’t take credit at the time.”

“Quite correct,” said Dumbledore, nodding. “But don’t you see, Harry, that if he intended the diary to be passed to, or planted on, some future Hogwarts student, he was being remarkably blasé about that precious fragment of his soul concealed within it. The point of a Horcrux is, as Professor Slughorn explained, to keep part of the self hidden and safe, not to fling it into somebody else’s path and run the risk that they might destroy it — as indeed happened: That particular fragment of soul is no more; you saw to that.

“The careless way in which Voldemort regarded this Horcrux seemed most ominous to me. It suggested that he must have made — or been planning to make — more Horcruxes, so that the loss of his first would not be so detrimental. I did not wish to believe it, but nothing else seemed to make sense.

Moreover it wasn’t supposed to be used to open the Chamber of Secrets without Voldemort giving such a directive:

“But I thought he meant Lucius Malfoy to smuggle it into Hogwarts?”

“Yes, he did, years ago, when he was sure he would be able to create more Horcruxes, but still Lucius was supposed to wait for Voldemort’s say-so, and he never received it, for Voldemort vanished shortly after giving him the diary.

“No doubt he thought that Lucius would not dare do anything with the Horcrux other than guard it carefully, but he was counting too much upon Lucius’s fear of a master who had been gone for years and whom Lucius believed dead. Of course, Lucius did not know what the diary really was. I understand that Voldemort had told him the diary would cause the Chamber of Secrets to reopen because it was cleverly enchanted. Had Lucius known he held a portion of his master’s soul in his hands, he would undoubtedly have treated it with more reverence — but instead he went ahead and carried out the old plan for his own ends: By planting the diary upon Arthur Weasley’s daughter, he hoped to discredit Arthur and get rid of a highly incriminating magical object in one stroke. Ah, poor Lucius... what with Voldemort’s fury about the fact that he threw away the Horcrux for his own gain, and the fiasco at the Ministry last year, I would not be surprised if he is not secretly glad to be safe in Azkaban at the moment.”

The free Death Eaters were not very loyal to Voldemort. Even if Lucius didn't know that the diary was a Horcrux, there were others who knew about Voldemort's immortality, which is evident from Voldemort's speech at the graveyard.

“And then I ask myself, but how could they have believed I would
not rise again? They, who knew the steps I took, long ago, to guard
myself against mortal death? They, who had seen proofs of the
immensity of my power in the times when I was mightier than any
wizard living?"

-Harry Potter and the Goblet of Fire

Moreover, Lucius's plot with the diary was not meant as a favour to Voldemort. It was simply meant to remove Dumbledore as headmaster, to remove him from a position of power. Lucius must have believed Voldemort truly dead, otherwise he wouldn't have risked the destruction of the diary for such a frivolous purpose.

Your supposition, that the diary "seemed to have come with a set of instructions on how to use it to bring Voldemort back," is incorrect. As Dumbledore explains in Half-Blood Prince, Lucius Malfoy had no idea the diary was a Horcrux or could be used to revive Voldemort. He was only told that the diary could be used to reopen the Chamber of Secrets and to smuggle it into Hogwarts when Voldemort ordered him to. Voldemort disappeared immediately afterwards and Malfoy repurposed the diary into a revenge plot against Arthur Weasley

"But I thought he meant Lucius Malfoy to smuggle it into Hogwarts?"

"Yes, he did, years ago, when he was sure he would be able to create more Horcruxes, but still Lucius was supposed to wait for Voldemort's say-so, and he never received it, for Voldemort vanished shortly after giving him the diary. No doubt he thought that Lucius would not dare do anything with the Horcrux other than guard it carefully, but he was counting too much upon Lucius’s fear of a master who had been gone for years and whom Lucius believed dead. Of course, Lucius did not know what the diary really was. I understand that Voldemort had told him the diary would cause the Chamber of Secrets to reopen because it was cleverly enchanted. Had Lucius known he held a portion of his master's soul in his hands, he would undoubtedly have treated it with more reverence — but instead he went ahead and carried out the old plan for his own ends. By planting the diary upon Arthur Weasley's daughter, he hoped to discredit Arthur and get rid of a highly incriminating magical object in one stroke."

To that last part, Malfoy tells Mr. Borgin in Chamber of Secrets that he's selling a whole bunch of Dark artifacts because he's worried about ongoing Ministry raids.

“You have heard, of course, that the Ministry is conducting more raids,” said Mr. Malfoy, taking a roll of parchment from his inside pocket and unraveling it for Mr. Borgin to read. “I have a few — ah — items at home that might embarrass me, if the Ministry were to call.…”

Mr. Borgin fixed a pair of pince-nez to his nose and looked down the list. “The Ministry wouldn’t presume to trouble you, sir, surely?”

Mr. Malfoy’s lip curled. “I have not been visited yet. The name Malfoy still commands a certain respect, yet the Ministry grows ever more meddlesome. There are rumors about a new Muggle Protection Act — no doubt that flea-bitten, Muggle-loving fool Arthur Weasley is behind it —”

So a few hours later, he runs into his hated foe, as his daughter who's going to Hogwarts, holding exactly the kind of Dark artifact he was planning on getting rid of anyway, and was told years earlier should be smuggled into Hogwarts on the command of a guy who "died" twelve years ago. Why not dump it?

It would have been very dangerous for any of the Death Eaters to do so,
as only a parselmouth would be able to communicate with the basilisk,
so it risked being a suicide mission. 
(The Death Eaters weren’t particularly known for bravery.)