The word coprosperity (or co-prosperity) was first used in English in the early 1940s as a translation of the Japanese 共栄 in the expression 大東亜共栄圏, and it is still used mainly in historic or ironic reference to that "Greater East Asia Coprosperity Sphere."
Perhaps out of historical embarrassment, no English-Japanese dictionary that I checked noted its origin or its most common usage:
The only English-English dictionaries listing the word seem to be the Oxford English Dictionary and its Shorter offspring.
━n (双方)共に栄えること, 共栄.
n. 相互繁栄，共栄; a ～ sphere 共栄圏
a co-prosperity sphere 共栄圏.
(December 11, 2004)