For a basic investigation, you only need a diaper, water* and graduated cylinder (or measuring cup). Just for fun, you could add a drop of yellow food coloring to your water supply... it might completely gross you out, but middle school boys will be completely sold on it!
To take the experiment one step further, you can compare the absorbency of different brands of diapers. Make sure you use the same size diaper for each brand. After gathering your results, you could even determine the diaper cost per mL of water held! Do the more expensive diapers hold more water? Remember, for the most accurate results, you should test several diapers of each brand.
*I've always seen this basic experiment done with plain water. But, if you'd like to simulate urine, mix 9 grams of salt into a liter of water and use that solution. I've read that the diaper will perform differently with this solution than with straight water. That sounds like an experiment worth trying!