How can I get my ally to like my potential ally in Stellaris?

Solution 1:

There is little you can do at the moment, it may be added in a DLC.

If they are rivals, they hate each other. Influencing how somebody feels about a third person was never something you could do a lot in Paradox games, but a feature like this may be added, when diplomacy gets expanded in a later dlc.

The best shot you'd have is to declare war on a rival of your potential ally. This may cause your ally to declare this empire its rival, with some luck your ally removes your potential ally from his rival list to do that and combined with the mutal rivals opinion bonus, that opens up the remote possibility of your ally and potential ally reconciling their differences. But it's a very long shot.