Make sure you and the AI in question both have Alliances, gift it to them if you must. To ally your relations with said AI must be at Close.

A few things are factored into your relations. Look in the Foreign Policy screen and under the report tab you will say realtion factors.

These are what are determining your level of relations.

Some may be,

They dont trust us,

Our militray strength

Trading

Ethical alingment

Diplomacy

Close Borders

Those are just a few, there are many factors. Look for those that have - next to them, these will be what is holding you back from achieving close relations with that AI. + and ++ means your doing well, try to do more of anything that is +.

The more ++ you have the better the relations, and try and rectify any of the -.

Allying with an AI of a different alignment can be tricky to do though so concentrate on similar ethical alignments as your self.

Hope this helps.