The " Option " you seek will reveal itself as one choice of several in a dialogue box that will appear on your screen after your Diplomat approaches another civ's city & tries to " enter " it.
The choice you need is called "inste a revolt", it is usually the last choice in a list that includes
" Investigate City " , "Steal technology" & " Industrial Sabotage".
"Buy a City" is just one of a few different ways the "option " is referred to among Civ Players.
There are a few other details such as paying twice the price to avoid an " incident " & the fact that some cities can not be Brought/Revolted, Capitol cities for instance, & the skill of the diplomat & condition of the city also factor into the price you pay. Spys get a lower price than Diplomats & Veterans do better than non - vets.