Level Balls (and other Apricorn Balls)
As of yet, the internet has found no other method to obtain more Apricon Balls, which kinda sucks.
When you run out of Beast Balls, Looker will give you more Beast Balls if you do not have any in your inventory. By letting all of your Pokemon hold the Beast Balls, you can basically get an infinite amount of Beast Balls (although it would require a hell of a lot of Pokemon to be caught. See source for a video).
Hope I helped. :)