King was put in charge of Ireland's final two World Cup qualifying matches after Giovanni Trapattoni left the position last month following two defeats that made reaching next summer's tournament almost impossible.
The 57-year-old's first match at the helm resulted in a 3-0 defeat at the hands of Germany yesterday, and Coleman is keen to send the temporary boss off with a victory to his name.
"We want to finish on a win. As players playing for your country, you want to win as many games as you can, but for Noel as well," Coleman told PA.
"He's come in for two games and it would be nice to get a victory for him. Hopefully on Tuesday night, we can show the other side of our game, how good we are on the ball at times, when we are at home to Kazakhstan."
Ireland have now lost three matches in a row and will finish the current qualifying campaign fourth in Group C.