How old are you?
It sounds pretty stupid that your parents might say that you are not allowed to unicycle. My mum and dad bought me a unicycle for my brithday. If they are going to be weird about it then just show them some of the really possitive threads on the forum and they might understand it a little better. You could show them this thread http://www.unicyclist.com/forums/showthread.php?t=68429 with the video about why people ride unicycles.
I hope that helps a little.