Is there a way to set which outpost serves which city?
As in a convenient part of the interface which would allow you to do this? No. However, there is a way to control which of your cities is served by a particular outpost: raze any city closer to the outpost than the city you want that outpost to serve. Is this a useful way to control which city benefits from an outpost? No, not really, but it will work. After all, if I recall correctly, outposts will service the closest same-faction city to them.
So, if you want every outpost to serve your capitol, it's just a simple matter of genocide (or slavery and probably some genocide, if you took the Slave Lords faction trait) and then there you go, every single outpost serves your capitol. Note: I don't recommend this path, as you'll end up really slowing down resource development, troop recruitment, and research, and probably kill your economy in the process.
I also wouldn't recommend razing cities in order to control the city served by the outpost, as this will probably cost you much more in terms of the economic hit you take from doing this than you gain from controlling the city served by the outpost.