David Talbot writes in The mother of all coverups:
On a White House tape recording, President Nixon is heard telling aides that the Warren Report "was the greatest hoax that has ever been perpetuated."
Does the tape of Nixon having said that the Warren Report on the assassination of John F. Kennedy was the greatest hoax that has ever been perpetuated really exist?
Nixon did use the words "the greatest hoax that has ever been perpetuated" in a recorded conversation related to the Kennedy assassination, but it wasn't in reference to the Warren Commission report. Rather, to Nixon, the "hoax" was the idea that a right wing group such as the John Birch Society was behind the assassination. (The Warren Report concluded that Oswald acted alone and not as part of any conspiracy.)
I think the original source of the mischaracterization of Nixon's words may be a BBC News article from March 1, 2002, entitled "Revelations and gaps on Nixon tapes" by Kevin Anderson. It is the earliest instance I've found of the "greatest hoax" line juxtaposed with a reference to the Warren Commission.
Referring to the report by the Warren Commission, "it was the greatest hoax that has ever been perpetuated," Nixon said. He did not elaborate why he questioned the report.
Anderson doesn't give exact details about the alleged conversation, but says that it took place in May of 1972, between Nixon, H.R. Haldeman, and Charles Colson, in the context of a discussion of the May 15, 1972 attempted assassination of George Wallace.
However, CNN ran a show on February 28, 2002, in which they apparently included a clip from the relevant recording, with more context. Their transcript has:
RICHARD NIXON, FMR. PRESIDENT OF THE UNITED STATES: Why don't we play the game a bit smarter for a change. They pinned the assassination of Kennedy on the right wing, the Birchers. It was done by a Communist and it was the greatest hoax that has ever been perpetuated. And I respectfully suggest, can't we pin this on one of theirs?
Ideally we would be able to confirm this with the actual audio recording or an official transcript. This is a bit tricky. The Nixon Library maintains the tape archive but they do not have posted transcripts or audio files for all of them, though they do have "subject logs" which summarize the topics discussed, and other metadata.
After a fair amount of digging, my best guess for the conversation in question is Conversation 339-4, recorded in the Executive Office Building on May 15, 1972 between 7:42pm and 8:10pm. It fits in several respects:
This was just a few hours after the Wallace assassination attempt, which took place at about 4pm on that same day per Washington Post.
The subject log on page 26 has "Wallace -Assassination attempt -Compared to John F. Kennedy assassination -The President’s view -Assailant -Political leanings -John Birch Society".
If I'm reading the log correctly, the preceding pages show that Haldeman and Colson were present.
A few lines further down is a log entry for "-Assailant -Possible story -The President’s instructions -McGovern-Kennedy supporter" which matches a quote in the BBC article ("Just say he was a supporter of McGovern and Kennedy") that's said to be from the same conversation.
The Nixon Library released tapes in several batches over the years. The period of January through June 1972 was the "3rd Chronological Release" on February 28, 2002, which matches the dates of the BBC and CNN reports.
The Nixon Library doesn't currently have recordings or transcripts posted for tape 339, but they do say they can provide copies upon request. Perhaps this is how the media got them in 2002.
However, there is a third-party website, nixontapes.org, which has what they claim to be audio files of most of the Nixon tapes, including all of the 3rd Chronological Release and tape 339 in particular. (It's odd that a third-party site would have this when the official site doesn't, but it's possible they obtained physical copies from the Nixon Library through their copy process, and digitized and/or uploaded them themselves. I'm willing to believe that their recordings are probably authentic, but a small grain of salt may be needed.)
The statement in question is at 1:47:25 in the 339a file (caution 110 MB download). The audio is reasonably clear and Nixon's voice is quite recognizable, and to my ear it matches the CNN transcript shown above. (And the "supporter of McGovern and Kennedy" line is a few sentences later, so this fits perfectly with the BBC article.)
