How to Spread Religion to a City-State

[HannibalBarka]

In the list of the request done by a CS there is :
Spread Religion – a City-State may ask you to spread your religion to them. This will require a Great Prophet or Missionary, and will require you to convert the majority of their citizens (which could mean you have to spread religion more than once). A side effect of this is that, as mentioned in the Religion section of this guide, your influence with City-States with which you share a religion degrades 25% slower than otherwise.

How am I supposed to do that? in the game I am playing, I founded Islam and many CS near me were asking for my religion to be majority religion in their city. I brought a Prophet and later a missionary but once they are in the CS area, the "Spred Faith" button is not available, it is actually available only in my capital (and later in my second city where i created the missionary). Am I supposed to click on the "Spread faith" button there and the faith will spread to "other" cities (hoping it will reach the CS I am targeting)? or is there some thing I am not doing correctly?

 

[Putmalk]

Move adjacent to the city and click "Spread Religion".

 

[Randall_Flagg]

Or wait until it spreads by itself, providing your religion is with 10 Hex's. I find the best way to get to city states, and more profitable to me was to spread to civs that were within 10 hex's. Granted it takes time, but missionaries are horrid, and profits are better used for Holy cities.