Few things to consider...
 You'd format the command to get the text + score on the same line something like this
Serial.print("Left Players score: ");
Serial.print(Right Players score: ");
 To clear the previous score, it depends on what you are "printing" to, for example are you viewing the output in the Arduino IDE, hyperterminal, processing, LCD, something else?
If you are using hyperterminal, there are clear line and clear screen commands you can send. You would do this just before sending the new score.