Well, since the first educator suggested the latter of the two Paul Newman movies, I will play devil's advocate and suggest the former. In my opinion, Ponyboy saw either The Hustler or Hud. These would fit well in the context of The Outsiders as well.
Yes, it's true that Ponyboy says, "I had only two things on my mind: Paul Newman, and a ride home." Because The Outsiders is set in the 1960s, I think it's more likely that the movie was one of the EARLY 1960s instead of the latter. (The latter 1960s suddenly switched to issues surrounding Vietnam and hippies. The Outsiders certainly isn't there yet. In fact, it has more in common with the late 1950s. So let's look at the two movies, for what their worth.
The Hustler was made in 1961 and stars Paul Newman as "Fast Eddie" ... a small-time pool hustler trying to turn big-time pool hustler. He does so, of course, but only after many conflicts. Fast Eddie stakes his entire 3k on his last game and wins (again and again), but is told never to enter the big-time pool hall again. Hud was made in 1963 and stars Paul Newman as Hud. In fact, the movie poster proclaims "Paul Newman IS 'Hud.'" Hud is a western that pits father (Homer) against son (Hud) during an outbreak of disease among the cattle. In the meantime, the younger nephew, Lonnie, is forced to choose between the two men.
The former (with its breaks with the law) and the latter (with its conflict between family members) would be a perfect movie for Ponyboy to watch during The Outsiders.