Rivet setter, page 3108, part numbers 6663A11 to 6663a21 at
www.mcmaster.com $18.60 or a bit more for larger sizes.

It has a hole the right size for the rivet body and a dimple to make the
nice rounded head. Set the rivet in the material, put the hole over the
rivet, give it a good smack to set the 2 sheets together, move over to
the dimple and finish the job.

Dave in MD wrote:

I need to peen over some 1/16" aluminum rivets, and was just wondering if
there is an ideal tool for this to get the shank to "mushroom" nicely?

Thanks for any advice,
Dave