Try Big Flats Rivet Company: http://www.bigflatsrivet.com/index.html
Find the largest size drill bit that will fit in the hole. If the hole is a shade under 3/32" (common size for little rivets) you can either drill out the hole or tap the rivet in. Use aluminum rivets. If they are loose you can either buck them by deforming them inside the head tube or put them in with a drop of loctite. A little trim adhesive (or rim glue)
on the badge itself will keep it on and the rivets will locate it accurately.