Eva Ibbotson's Journey to the River Sea is a novel set mainly in the Amazon region of Brazil. It's clearly set quite some time before its publication date of 2001, what with a "governess" being a major character; but it must also be set after the 1880s, given the existence of Little Lord Fauntleroy as a stage play in the story. Wikipedia says it's set "early in the twentieth century", but gives neither a source for this claim nor a more specific period.
When was the book set? Let's see how narrow we can get the range.