My knowledge of history is pretty poor, but the scenario you describe here can't be applied to China, can it? I don't have any knowledge of the U.S. trying to encourage a coup there...

China became communist due to a coup (of sorts) in 1949. The US didn't recognize the new Communist government in China until 1972 (or so), instead pretending that the Nationalists in ``exile'' in Taiwan were still the legitimate government of China.

So no, they encouraged no coup, but that was a legitimate people's uprising, as it was in Cuba. No coup probably could have been fomented. In both cases, the former governments were incompetent to corrupt.