Well, if you construe (or miscontrue) the reason the Secret Service was founded in the movie 'The Wild, Wild West' that would present one possible answer.
It just may be easier that an American incarnation of the Diogenes Club is founded in post-ACW America.
One way would be to have one of the European powers outright support the CSA instead of the largely backroom aid that they originally gave them. The CSA can still lose, but the act of Europe poking it's noise into American affairs probably will be enough to get the Union rather paranoid.
what about a bigger interest in China or SE Asia outside of Phillipines? or possibly the purchase of Greenland. these events I think by nature would require a larger OSS. I think with entanglement comes a need to know what your rivals are up to