Movies can be a nice gift for someone who isn't feeling well because they are a good distraction and require little effort to watch. If the child is young or particularly sensitive you should screen the movie yourself before giving.
Here is a list of ecology-themed movies for kids. The list is from 2008, but these are popular movies so they should be available. Perhaps your gift could be a promise of a succession of movies you've rented from Netflix!
Grinning Planet has a list of environmental movies which may be suitable for a teenager. (You should probably try to avoid the depressing ones and the few which are are intense "eco-horror" films.) Image of Finding Nemo is from rottontomatoes.com