Did the name "白俄罗斯" for Belarus exist in Chinese language before 1991 or was it created only when Belarus became an independent state in 1991?
the internet archive has the book 瀛環志畧, in volume 4, "白峩" was used to translate belarus:
this book was published in 1849.
the 峩 (u+5ce9) was a variant of 峨 (u+5ce8), both of them share the same pronunciation with the character 俄 (u+4fc4), that is used in modern days translation.
then, the internet archive has another book 海國圖志, in volume 54, "白峩羅斯" was used in lieu of belarus:
this book was published in 1843, maybe the first geographic / atlas type of book in imperial china.
btw, minsk was translated as "閔士其" :)
have fun :)
Presumably it already existed. Prior to the present-day republic, there was the Belarusian People's Republic, the Socialist Soviet Republic of Byelorussia, and the Byelorussian Soviet Socialist Republic. All of the official Chinese names for these states/provinces include 白俄罗斯. There seem to be pre-1991 Chinese books that use the term, but Google Books is not a perfect source.