There are two ways to rejigger the scoring. Either you can eliminate scores from the top - so the scores run, say, from 0 to 10 - or from the bottom - so the scores run from 1-12. Either works, but I think that the former is better because it is more personally satisfying to give a song 0 points than it is to give it 12. Top score is top score whatever the number is, but zero is always zero.
Of course, if you have more players than you need, you can add additional zeroes, just like the real Eurovision.