Or something like this Rapidfire shifter, where you can use your thumb to shift up and down. - Shimano Altus Shifter 7 Speed Right Rapid Fire MTB Mountain Bike Vintage | eBay

I had those on my Schwinn crosscut, but they were the integrated version like pictured below (shimano exage 400 LX). They were amazingly simple. Not sure how easy the shifter above could be found though, unless you'd be willing to consider integrated ones. The linked one is quite expensive. I think the acera and altus shifters would be great though, and much easier than those tourneys on there already,

integrated ones i had on my Crosscut -