Hello Annie
Hopefully you will get several replies, but here is my pennyworth.
If you are spending some time applying acrylic paint, it may be quicker and easier to give it a layer of white paper - just as easy as a coat of white paint. It certainly wouldn't be starting again, just adding one more layer.  You would probably need to use more PVA than other paste in order to adhere over the paint. 
An alternative would be to apply a coat of a good primer, perhaps adding an undercoat to give really solid cover.
Good luck.

I agree that the problem might be your paint (too thin perhaps).  After three layers, the paint should be obscuring the underlying newspaper text/images pretty well, if not completely.  White and yellow do tend to be the most problematic colors for showing through.

It is indeed best to do the outer layer in bare newsprint, or prime it in white or light gray, if possible, before applying lighter colored paints, but, as you indicated, it's kind of too late for that now (although you could go over your existing painted surface with one more layer of bare paper and try painting them all over again.)  It might be a tedious business, but if the quantity of paint used isn't a concern, you could just keep adding more layers, eventually your students will succeed.

Another thing you could try is getting a bunch of color magazines/newspapers and decoupaging the surfaces in the colors you want instead of painting them (i.e., gluing on yellow colored paper to the areas you want to be yellow, and so forth.)