The best replacement for rivets is bolts.

The best alternatives to rivets are rated as following:
★★★★★  bolts
★★★  welds
★★★  welding
★★  screws
★  chicago screws
★  sheet metal screws
  blind
  aluminum rivets
  grommets

Your alternative for rivets is not listed? Suggest!
Speaking about rivets, one probably shouldn't forget about rivet gun.

Other search terms related to rivets and their ratings are:
★★★★★ rivet gun
★★★ rhinestones
You have in mind a companion for rivets and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of rivets in all years. Click on graph for more.
rivets
bolts
welds