Since my team has already lost, making me ineligible for the best prize, I will reveal my secret Altadorian technique for scoring with any ball on anybody. (Yeah, I'm tired of waiting for King Altador to show up at my door and ask me to help him build a new kingdom.) This technique assumes your players have some speed. Altador was a pretty fast team.
If you'll excuse my crude drawing, here it is:
http://img144.imageshack.us/img144/2438/scoring3vi.png
Step 1 is something everybody is probably familiar with already. You win the faceoff (best thing to do to save time) or you intercept/steal the ball from your opponent. Run towards either side of the opponent's goal posts. What you want to do is draw their goalie as far away from the middle of the goal as possible. In the drawing, the dark blue circle is the opposing goalie being drawn to the end of his goal due to my player's running diagonal down.
After completing step 1, you have the option of shooting the ball diagonally up towards the vacant areas of the goal. This generally works with all the balls except the faerieball and saves a little bit of time from the rest of the technique. However, there's the chance you'll overshoot the far corner and miss the goal.
If you choose not to shoot after step 1 or have a faerieball, step 2 is to run up (or down, depending on your directional heading) past the goalie and across the goal. If your player is fast enough, you will outrun the goalie and put a bodycheck on him.
Step 3 is, once you have proper position on the goalie (as shown in the actual screenshot [I was running down from the top of the screen]), just shoot the ball in. Or sometimes another computer player will push you in the back, knocking the ball loose and into the goal. These are point blank shots. As long as you have good positioning versus their goalie, they cannot miss no matter what ball you're using. I didn't demonstrate it as well in this screenshot, but you can actually angle your player to run until he/she is right alongside the goalie, preventing the goalie from moving down (or up) and interfering with or possibly blocking your shot, which is what I mean by a bodycheck. Just don't flash the ball directly in the goalie's direction or it might get stolen from you. This screenshot has me a little farther away from the goalie, but I'm still wide open and able to get the job done with an uncontestable shot.
Maybe Neopets will see this lapse in their rules or AI defense and correct this. In real life hockey and soccer, I don't think you can bodycheck or even touch the goaltender like this. I think they consider it interference.