I've had two experiences with mounting headbadges without proper rivets. One went south and the other was a "smashing" success. Both were performed by experienced local mechanics.
1. The failure. I was putting the finishing touches on a Bottechia mixte for my niece (a frame generously donated to me by CR member Terry McClintock). I was happy I had found a headbadge on ebay and paid $25 for it. The mechanic attached the badge using a "never-fail" method of strong, double-sided adhesive tape. I made no comment, but was internally skeptical. While driving to deliver the bike for my niece's birthday, the headbadge blew off somewhere on the Interstate, never to be seen again. The event marred an otherwise happy occasion, and I had to finally source another badge for twice the money.
2. The success. A different mechanic at a different shop, when attaching a badge to another bike, used the little metal caps put on the end of brake and shift cables to make them look tidy and prevent them from fraying. You know, the things you normally squeeze onto the cable ends with pliers. He inserted the caps closed-end first through the badge and into the head tube, then tapped or "smashed" the open ends flat so they splayed out and secured the badge. Perfect hold, and darn-near perfect look, too. If you can't find new caps, just rob one from a junker bike of yours and there ye go!
Hope this helps.
> From: firstname.lastname@example.org <email@example.com>
\r?\n> Subject: [CR] Mounting headbadges!
\r?\n> To: Classicrendezvous@bikelist.org
\r?\n> Date: Friday, July 24, 2009, 7:32 PM
\r?\n> I've ordered some genuine Raleigh
\r?\n> headbadge rivets from England, but it'll probably take weeks
\r?\n> for them to get here, in the meantime, I found a source for
\r?\n> brass pop-rivets or "blind rivets" of the correct size. I
\r?\n> was wondering if you guys have had any experience remounting
\r?\n> headbadges and what techniques you used.
\r?\n> Fred Durrette
\r?\n> Summerville, SC