To be precise, the Beale Papers comprise not one long ciphertext (putting the VMs' thorny Currier A-B language continuum issue to one side) but three short codetexts, all allegedly dating from 1819-1821: part 2 was publicly announced in 1885 already solved (for its codebook, the encoder used a slightly mangled/miscopied version of the Declaration of Independence)... but the directions to the buried treasure were in the undecoded part 1, while the shorter (and also undecoded) part 3 listed the people involved. Of course, only someone who has broken the two remaining codes would know if all of this is true or not. :-)
So, it's basically a kind of Wild West bandit take on a pirate treasure map (which to me sounds like an Alias Smith and Jones script, oh well) but made obscure with some kind of dictionary code: all of which is reassuringly familiar if you've just read PopCo. Confusingly, some people argue that the Beale Papers are a fake (possibly by the promoter of the 1885 pamphlet, or even by Edgar Allen Poe, etc), claiming justification from statistical aspects of the cryptography and/or on claimed anachronisms in the language, etc: but a definitive answer either way has yet to be found.
For what it's worth... my opinion is that, as with the VMs, cries of hoax are more Chicken Licken than anything approaching an ironic postmodernist reading. Really, it does look and feel basically how a home-cooked Victorian code-text ought to, with an emphasis towards lowish numbers (up to 350) plus a sprinkling of higher numbers (possibly for rare or awkward letters): Jim Gillogly's observation (in October 1980 Cryptologia) of an alphabet-like pattern in part 1 (if you apply part 2's codebook) seems to me more like a clue than a reason to reject the whole object as a hoax. As an aside, a few years ago I heard (off-Net) whispers of one particular cryptographic solution that had yet to be made public: but Louis Kruh in Cryptologia reported several such plausible-looking solutions as far back as 1982, so what can you say?
However, all of this is an entirely different claim to the "Beale Solved" code solution linked above, which was (re)constructed by Beale treasure hunter Daniel Cole (who died in 2001). Even though the dig that was carried out as a result of Cole's decryption revealed an empty chamber (the website claims), the cryptographic details (ie, of how the codetext links with the plaintext) have yet to be released... which is a tad fishy.
A quick check of the first page of Cole's version of part 3 reveals that he didn't read it as a simple cipher or codebook, because repeated code-numbers only rarely get decoded as the same letter (for example, the five instances of '96' get decoded as "s / e / r / h / n"). Yet this seems somewhat odd: if there was some kind of strange offsetting going on, the distribution of code-numbers would not need to so closely resemble the kind of distribution you see in code book ciphers.
But once you confess to having taken a single step down the whole "it's actually a strange cipher pretending to be a codebook code" route, nobody will believe a word you say, right?