These are the two best attempts, 6 and 12, out of 12 the day I decided to make it so I could answer "Yes!" to the people who ask me "I've seen you ride your unicycle to work, can you juggle while you're riding it?" The twelve attempts took about 14 and a half minutes.
I learned to ride a unicycle when I was 19 and I learned to juggle three balls at about the same time. I spent quite a bit of time riding the uni around the UC Davis campus in those days and juggling at the same time. I started to juggle clubs in the early Summer of 2009.
In order to facilitate juggling on this unicycle it has the seat post extended as far as possible and still be able to still steer the uni but not conveniently, and I replaced the six inch crank arms with four inch crank arms. It's not nice to strike your knees while juggling and even with the uni set up this way I have to pay attention to avoiding my knees. (But that's true of walking while juggling too -- especially on stairs.)