Usually, I put them on training mode (Siphon or Unrest) to reach level 3. I tend to pick the worst Promotion for the first two ones. A master Spy gain +2 diplomatic level access instead of 1, so +6 Combat Strength instead of 1. They will usually run Listen Post when at War, or Siphon Funds. Steal Tech Boost when behind, and Great Work Heist if I need some Great Works (it is simpler to buy, but not when denounced). The AI tends to shuffle their Great Works at random, ending the mission prematurely.
Sabotage and Recruit Partisans feel to dangerous to do for what they do.
Then I will try to get my "City-State" Spy: Ace Driver (+4 level to escape: CS don't take prisoners), Disguise (Takes no time to establish), Linguist (-25% time) or Smear Campaign (+2 level on City-State). At level 3, they remove 6 Envoys at once. Be careful: a City-State an AI has no Envoys in is more likely to get conquered.
Also, I will try to get my "home" Spy: Quartermaster (+1 level to all Spies when at home), Polygraph (-1 level to all enemy Spies when at home), Surveillance (+1 level counterspy / all districts in city are protected) or Seduction (+2 level counterspy). I tend to set-up a well placed coastal cities with Reyna, Commercial Hub + Harbor, Diplomatic Quarter and Encampment. This is my Spy trap. If the AI wants to do something, they will go there so my Industrial Zone or Governors are "safe".