~~They cannot touch the cup or ball with any part of their body.~~
The only way I know of to complete this task is to apply Bernoulli's Principle by blowing across the top of the cup and ball, allowing the ball to rise.
If that's too easy, you can add a second step to the challenge and have the students move the ball from one cup to another without touching anything.
*Try out the cup you plan to use ahead of time. If the cup is too deep, it won't work. If you use a paper cup, you can always cut the sides down. But, be careful, if the cup is too shallow, students will just blow the ball out and not put Bernoulli to use. I found that a cordial glass (see below for a cordial glass story) works well, if you have one shaped like mine!
Here's the story... when we were little (like, before we started school), my cousins, brother and I drank apple juice out of mini wine glasses at my Grandma's on special occasions, like Easter. I was in college before I realized that those glasses were not in fact miniature wine glasses made for small children to use when the grown ups were drinking wine, but were really cordial glasses. :) Who knew?!?!