The elephant's rate is 0.005 - 0.015. This means that it's random and can be anywhere from 67 turns or so to 200 to generate one elephant.

They are extremely rare. The easier way is to play a Roman faction and satisfy diligently the missions that give a major exotic unit as a reward.

I got two of those from the Senate in my Brutii game which I later used to kill the Senate. Ahhh the irony.