I never have a problem DOF'ing almost everyone. I think the main points are: trade routes, open borders, DON'T spread a religion, and, if you can afford it . . . go ahead and let them have that Sugar for 30 turns free of charge. If you wont go near unhappiness from losing a luxury and the ask for it (even if it's the last unit), give it. This helps the AI to slaughter eachother when their enemy inevitably asks you for some resources as well. The plot only thickens when you have diplomats in many capitals, and share your intrigue with all the AIs. Create war between them and maintain yourself as everyone's best friend and financier!
Settling close to an AI will have different effects based on how much space is available total. If you settle close to an AI that has little room elsewhere, gird thy loins.