After powder coating my daughter's '81 Fuji, I used the heads of some extra stainless steel spokes as faux rivets, held in place by epoxy.

I cut off the spoke head with a Dremel, leaving maybe 3/16" of the spoke shaft. I put some epoxy in the head tube's holes, inserted my faux rivets, and mashed the epoxy into place firmly with my fingers from inside the head tube.

There's also a touch of contact cement between the badge and the head tube to stick the badge in place and prevent the potential for rattles.