Down in the dumps
'The dumps' wasn't a place but a commonplace medieval expression meaning dejection; melancholy; depression. The earliest printed record of it that I have found is in Henry More's A dialoge of comforte against tribulation, 1529:
What heapes of heauynesse, hathe of late fallen amonge vs alreadye, with whiche some of our poore familye bee fallen into suche dumpes.
Dumps was used frequently in plays and manuscripts from the 16th century onward. Shakespeare used the term several times, for example, in The Taming of the Shrew, 1596:
Why, how now, daughter Katharina! in your dumps?
To be 'in the dumps' was to be dejected and depressed - what Sir Winston Churchill was later to call 'black dog'. The first record we have of 'down in the dumps' is in Francis Grose's invaluable dictionary The Dictionary of the Vulgar Tongue, 1785:
DUMPS. Down in the dumps; low-spirited, melancholy: jocularly said to be derived from Dumpos, a king of Egypt, who died of melancholy.
Grose may have picked up the nonsense notion of a royal Egyptian source from a work by the early 18th century English poet John Gay. His poem Wednesday; or, the Dumps was widely printed with the following note inserted into the title:
Note: Dumps, or Dumbs, made use of to express a fit of the Sullens. Some have pretended that it is derived from Dumops, a King of Egypt, who built a Pyramid, and dy'd of Melancholy. So Mopes after the same manner is thought to have come from Merops, another Egyptian King who dy'd of the same distemper; but our English Antiquaries have conjectured that Dumps, which is, a grievous heaviness of spirits, comes from the word Dumplin, the heaviest kind of pudding that is eaten in this country, much used in Norfolk, and other counties of England.
When the note was added, or by whom, isn't clear and it could be that it came later than Grose's dictionary. Either way, it doesn't really matter, as the derivation of 'the dumps' wasn't Dumpos, or Dumops, (the correct spelling hardly matters either as the so-called 'King' never existed), nor was 'mope' derived from Merops.
The other suggestion raised by the spurious note - that 'dumps' derives from 'dumplin', that is, dumpling, is at first sight at least plausible. Dumplins certainly sound heavy going in a culinary sense - the OED defines them as "A kind of pudding consisting of a mass of paste or dough, more or less globular in form, either plain and boiled". They couldn't have been the source of 'the dumps' though - they weren't known until well after that expression was in common use.
See also: in the doldrums.