There are only 8 Unicorn baits.

I'm not sure why it would say 9. There are only 8 boxes of Unicorn bait, I'm certain on that part.
Exactly what does your Quest Log say? What is it telling you that you need to do for this Quest? What is telling you that there are 9 of them?

I can't remember if this was split up into more than one Quest (I do think it was though), and this Quest should be what the info is showing for when you click your King's Quest icon below your Level/XP bar. There is more than one part to it from the start of finding the boxes of bait to actually capturing the Unicorn. First, you have to complete all of the 8 puzzles that have the 8 boxes of Unicorn Bait, collecting each one by whacking it 3 times just like you would to capture a Puzzle Monster - sounds like you have all of those puzzles completed. Did you actually collect each of the 8 purple boxes by whacking them each 3 times? If you did, then your Inventory should show that you have 8 boxes of Unicorn Bait. After that, you have to go on a Quest to place all of these 8 boxes of bait on the ground by following a trail and clicking on blues X's to place them. Then, you get the Quest to actually capture the Unicorn.

So, in order for me to be able to try to be of any further help, I need to know just what your Quest Log is telling you right now for this Quest.