Maybe there's a different mechanic to explore here that would end up with something along the desired results without having to re-implement Espionage...
I really like the idea of boosting CoE a bit, adding in a spy aspect and giving them a Disciple line.
So...going along with the Night Mother unit (not bad name at all for a CoE priest) and the Speakeasy building (which probably does need to be changed. Hall of Shadows? Whatever. That's bad...but you get the idea).
Why not give the Night Mother the ability to go to another Civ's city and create a building - the Hall of Shadows - there? It would of course consume the unit - after all, the Night Mother is now in that other civ's city spying and spreading dissension...
Effects? +15% to the crime rate, maybe 1 unhappiness (might be too much), and the ability to literally spy on the enemy city. Double click on it, see what buildings have been made there etc...much like the Shadow unit does, but this is a permanent effect.
There could be a gold siphon, 1 g per turn back to you, or a research penalty (how did those documents get lost/who killed that Sage?). Nothing too severe of course...but just ideas to play along with.
I do not think this should spread CoE to the city.
Probably could write some new events around this as well...for starters, an event that let's the other civ get rid of the Hall of Shadows in thier city. You know, someone spilled the beans to the Watch Commander, and in the middle of the day (because that's when all the CoE followers are asleep) they raided the place and chopped off a bunch of heads.
Edit: I'd also like to see CoE get the next step in Disciples as well...the rank 6 updgrade to the national unit like other religions get...so what do those units do? Probably something along the same lines, except with pretty drastic effects. Stick that unit in a city and cause instant unrest for 5 turns, or 10 unhappiness etc until the unit is moved (or killed), or perhaps bring something like the espionage event into play (you know that event, pay money for 4 improvements to be destroyed...) except that you can do this at will when you bring that unit into a city...click the button, 4 improvements get destroyed and you get the gold from them as if you had pillaged them (which is pretty much what you did). All this sounds fairly overpowered, so it needs some tempering...but just putting the ideas out there.