Civil War gear always has brass rivets.
Nate, good observation but the rivets used were copper. The specifications in the US Army manuals of the period called for copper rivets to be used at all times, no mention of brass.
As far as a time frame? As others have said, hundreds of years (at least) but riveting is not considered as strong a sewing and the commonly available rivets of today, called "copper belt rivets and burrs", have probably only been available for about 150 years. Maybe Chuck has better information?