Open Borders - One needs to have semi good relationship with in order to initiate this agreement. Should you already have an agreement with the faction, one won't be able to initiate another agreement until that one expired. Some tech trees may even require one to research basic diplomacy for this option.
Peace Treaty - In order to initiate a peace treaty one must be at war. There is also a cool down period (I believe 20 turns) before that AI faction will even speak to you about any options. The AI will also have to see peace with you as a viable option, if you are weak and they are destroying you, most likely they won't entertain this option.
Non-Agression Pact - Basic Diplomacy must be researched as well as appropriate diplomacy tech to unlock. Good standing with other faction.
Free Trade - Need to have a great relationship with other faction. Need to research economic treaty.
Research Treaty - Same as above but, need to research research treaty.
Culture Treaty - Same as above but, need to research Culture treaty.
Ally - Very good standing, most likely has one if not more of the above.
