This may have been covered before, but I just ran into this and thought I'd bring it up.

It's easy to see when a civ is aiming for a diplomatic victory: lots of city-state alliances, hurried progression to the Modern Era and the UN. The other AI civs should react to this by trying their best to ensure that the target civ doesn't get the necessary number of votes.

When the target civ's strategy becomes clear, the other AIs should (if at all possible in their situations) try to either buy alliances or conquer city states already allied with the soon-to-be diplo victory civ. If the UN has already been built and a vote is coming up, they should try their damndest to buy alliances instead of, for example, setting up expensive new research agreements that will be worth nought if one civ gets the necessary votes.

In general, the AI reactions to the victory condition approaches of other civs should be a lot more determined.