Rivets will work, you just have to get appropriate exploding rivets
Small Head 3/16 Inch Exploding Rivets - Speedway Motors, America's Oldest Speed Shop
Gm sends exploding rivets similar to this along with their front license plate brackets.
Online it seems like they run $0.08-$0.15ea and you're usually looking at buying 250, only ones I've seen in retail stores are around $1ea