There are certain conditions to the Pokeball that will be passed down:
-->if the mother Pokemon was caught in a Safari Ball, then your egg will also be in a Safari Ball.
-->if the mother Pokemon is Ditto, the ball will be a Pokeball by default.
PS - In the Friend Safari, you cannot catch Pokemon in Safari Balls, as these balls are not even present in-game until a transfer from the older generations of the game.
Source: Experience (I breeded a female Diglett in a level ball with a some other Pokemon, and my resulting Diglett was also in a Level Ball)
Hope I helped!