When we went to a party dressed as punks, we bought some blue hair spray from the local fancy dress shop, although you may be able to buy some in Woolworths or Wilkinsons. Good luck & have fun!
To dye it properly you'd need to bleach the beard first so that the purple colour will take and even then it's not guaranteed that the colour will be even/the colour you want/last very long. Probably best to stick to spray or something becuase when the purple fades you'll be left with a bleached beard...