We must first remember the fact that, at the time Karl Marx wrote his Das Kapital work, it was approximately twelve years after Eschwege died, as these are keys to be able to understand which would be the chief accuracy here... As it happens, the claim you presented itself contains major hints as to its authentic, primary source. (In actuality, as it turns out, only one source.)
There are currently four known selected works that are known to belong to Eschwege, all of which were originally published in German. (Several years before Marx had "Das Kapital" published.)
Hence, it is most plausible to think that because Eschwege dies in 1855 - years prior to "Das Kapital" being published, and also due to the fact that Marx adds a claim from Eschwege to his book - that he must have acquired the claim by written words... or books, by Eschwege himself. And so Marx had, most likely, all four of his works.
One: The year 1823
The year 1823 is the recorded year, and was the year in which Eschwege recalled that the "total produce of the Brazilian diamond mines for the eighty years ending in 1823 still did not amount to the price of 1 1/2 years’ average product of the sugar and coffee plantations of the same country...."
Two: His last two selected works
Consequently, the entirety of the account can be found in two of Wilhelm Ludwig von Eschwege's books : "Pluto brasiliensis: eine reihe von abhandlungen über Brasiliens gold-, diamanten- und anderen mineralischen reichthum" - from 1833, Pluto brasiliensis: a series of treatises on Brazil's gold, diamonds and other mineral riches. (And: "Beiträge zur gebirgskunde Brasiliens" - from 1832, Contributions to the orography of Brazil.
(So, as you can see, there is no Brazilian claim, but rather a report in German, by Eschwege, in his last two works.)
I did not include it here because I do not know German, and could not find a translation in English.... Only the titles were I able to include in my answer. However, I am positive that it is written in the books. (Ah, well, I'll leave it up to you to explore them..)