Great! I had been looking at that tool (a "sash balance rivet setting tool", which doesn't sound_ like it would work, but sure looks about right). I tried to order the official hand-punch from the company that makes the actual rivets, but they recently discontinued the tool, so I was SOL. I ended up having to use a combination of two other punches: A center-punch and a pin-punch, the first to spread the collar of the rivet, and the second to flatten the collar down. That worked, but imperfectly (the collar ended up with some cracks).

I have ordered this tool from Amazon, and will try it out: Thanks for the confirmation!

A piece of wood or other surface with a slight bit of give is adequate: The rivets are brass or aluminum, and are very soft, so you really don't need the "proper" female die for the head-side. That's my experience anyways.