I get to see a lot of old guns and it seems lots, if not most, have copper rivets. A lot have brass rivets instead, but very few brass mounted guns have iron rivets.
For modern makers I guess the material would depend on the look you're trying to achieve.
On the other hand, if you're copying a particular old makers style, I'd put the rivet, or rivets, in the location he used, and use the material he used.
John