I don't think it's ever been mentioned. I would expect Rafiki to keep a record of some sort mostrando the royal timeline, so maybe he knows!
In the movies, nothing is known before Mufasa and Scar's generation, but it is noted that Mufasa is definitely not the first king of the pride (e.g. "the great kings of the past" - suggesting there have been many before him).
Also, in the libros Mufasa and Scar had a generation before them; Ahadi and Uru. There was even an older generation with a king called Mohatu. This information's not been confirmed por the movie creators though, but it's interesting anyhow.
We do know that the latest generation is Kiara and Kovu, for now at least. In one of the SP books, it words the ending something like "the circulo, círculo of life was complete once again", suggesting that they would soon be starting a family of their own. Even if tu only go por the films, I think people still tend to presume that Kiara and Kovu will most likely be parents themselves someday!