Any simple experiment with an H-alpha telescope?
If you have the right filters and equipment you can make doppler measurements of the $H_\alpha$ line from the sun. Since an H-alpha telescope directly detects this you can use this to measure the doppler shift. Using this you can measure the rotation rate of the sun. This has been done before with a different telescope and the paper is here. 

It should also be noted that if you don't find an adequate experiment just seeing the sun thru your telescope makes a profound impact on the viewer. One writer wrote that " I watched with a mix of awe and fear. Ever since that time, I've seen the Sun not so much as a sunny companion but as a star to be reckoned with."
Reference is here. That link and this one discuss viewing the doppler effect using an H-alpha telescope.