Rembrandt did over 90 self portraits. He also had a box of costumes that he would either put on himself or a sitter when he did portraits. Perhaps you can have the kids put on "costume hats", take a picture of them, give them their picture and have them make a simple painting of themselves in the costume hat. (Ask your faculty to bring in a variety of hats, as well as kids, and put them in a box). Also his portraits are 3/4 turn. Depending on the age level of your kids (if they are elementary, which I think you had mentioned), you could actually make a template for them on the 3/4 pose that they could work of off.
Look at this work. Find similarities..fur, lush fabrics, gold chains...add these to the costume box as well. I would have this project be a combination of 'drama and art', and play up the 'character' aspect of the portrait.
Also, he is known for chiaroscuro (coming out of the darkness into the light). Perhaps you could have your students pose with the lights turned off, and a flashlight as the light source (especially when you take the picture as suggested above).