I learn't on a PA-38, and found it easy to land - eaiser than the Warrior.
The aircraft tail configuration may be the root of your problems, since it is out of the prop wash. Therefore, reducing power does not make a notable difference to the airflow of over the tail. This can often lead to ballooning etc. If you do balloon, hold it in the position, don't slam the nose back towards the deck.
Your other problem may be the underuse of rudder. I was very agressive with the rudder, keep the wings level, and just use rudder to get you on the centerline. Keep the thing in balance, and crab to the threshold. When I mean aggressive, I mean really take control.
So, when you know you'll make the runway, pull off all the power, keep the attitude in level flight, wings level - you will descend. Use rudder. Slowly bring the nose back 10 ft from the deck, and keep bringing it back until touchdown. If you balloon, hold the position, you will sink again.
Hope that helps.