Are you familiar with rivets sets, Dave? They're the tool made for the job.

Ed is right on, but if you only have a few to do you might consider making a
tool for the job. You can take a piece of rod, 1/4 to 3/8 would do, and make a
hemispherical depression in the end of it. You could put it in a lathe and
use a 1/8 ball end mill to make the depression for a 1/16 rivet. Don't go too
deep, make it a hemisphere. As Ed said, I would start with a ball peen hammer
just to get the edges slightly rolled over, then go with your home made rivet
set. This isn't going to last long, it isn't hardened, but it should last for
a hand full of rivets. Good Luck!
Rick