What about the simple toss of a coin? Heads or Tails? or getting out a pack of cards and the first one to draw an ace is determined the winner.
Seriously though I hate penalties ( apart from when one is awarded in regulation time ) it could well mean that the players that miss the penalties may end up being vilified by their own supporters but at the same time we cannot really blame them for missing what we would not want to do ourselves ( lets face it guys & gals it takes an awful lot of bottle to stand there and take one ).
I don't know if there are any alternatives apart from maybe replaying the game ( there used to be cup final replays all the time - we featured in two cup final replays ourselves in the early 80's ).