I am unaware of a regular unicycle, but if you have a book that lists one as an item, just take its weight in pounds, multiply that by 500gp, and add it to the base price (assuming the listed item is constructed of metal to begin with, and not wood). Mithral is automatically masterwork.
Assuming it's a mundane item, and not magical, it should be always available.
Unfortunately, there is no custom items allowed in PFS - so there is no legal way to create the unicycle:
Neither the craft feats nor the item creation section
of the magic items chapter in the Core Rulebook are legal
for play. Additionally, except for specific examples cited
in this guide or the Pathfinder Society FAQ, crafting of
mundane items is not allowed in Pathfinder Society.
- pg 8 of the v5.x Guide to Organized play
I imagine you would also need the "Perform" trick trained as well.
To re-write the original post I had up:
I have seen unicycles in PFS sanctioned play. While I realize this doesn't automatically grant access to the vehicle, it does set precedent: they do exist.
Now, they were on a not very formidable foe, and my general reaction was "how quaint," I assume that there is some manufacturer of one-wheeled bicycles.
Good luck getting the mithral unicycle, and good luck making that viable for play. The bears were trained on the unicycle and could use it for a spring attack, but failed ride checks/acrobatics checks when they needed to make them.
This is from an adventure I ran. The bear animal companion wanted to move by a half orc without provoking an apology. The acrobatics check roll was a 23, causing me to comment that the bear went down the stairs and around the half orc on a unicycle. The orc didn't die from the damage, but from embarrassment.
Imagine the conversation in the underworld: "how did you die?" "Well, there's this bear in a unicycle ...."