I doubt you'll be able to buy a specific rivet for it, at least, not from a bike shop, but you can make a rivet out of a bolt or a nail - it just needs to be exactly the same diameter. I've got an old Gran Sport but I've never sheared a rivet. From your photo it looks as if the rivet passes through small brass bushes - gentley tap the broken rivet out and get something the same diameter and cut it down to the right length, rivet one end over while in a vise, reasemble the mech, then rivet the other end over.
Love your forum name btw.