First, perhaps you should learn a little bit about how judging is done. Judges don't just 'allow' and 'disallow' stuff; well, at least that is not what they are supposed to be doing and the appeals system, essential for due process, is pretty good at correcting those who do that. Justice Cardozo wrote a great short book about it: The Nature Of The Judicial Process.

Second, 'Bitcoin', and resulting 'bitcoins', are really just a math equation and results of that equation. Obviously, neither the equation '2+2=4' nor '4' are not copyrightable. However, if you use a particular font, color, etc. and fix it in a medium then you may be able to have a copyright attach to that particular work. Copyright is a very abstract area of law in that sense. Consequently, copyrighting the math equation that is Bitcoin is, almost without a doubt, going to fail just like you would fail with trying to copyright the general formula '2+2=4'.

Likewise, with the other responses I do not think the contract theory is going to work either. However, one may be able to pin a property ownership theory after receiving it via contract; although I think this may be slim. Basically, receiving via contract bitcoins would be like receiving via contract the fox from Pierson. But even this analogy would be pretty weak and likely fail.