Great question. Takes some ingenuity. I've refinished several Raleigh's. This is how I solved the problem:
Go to a well stocked hardware store. Pick up some very small philips head silver screws. You will need to carefully look at them to get a similar diameter head to the original rivet. Go home. Place the threaded part of the screw in a pair of vice grips. Then put the vice grips in a vise with the screw head facing up. Carefully drill out the philips slots to create a round recess in the top of the head. Then sand the head down so that it is more flat. This will leave you with a screw head very much like what the rivet looked like. You may want to fill in the recess with some black paint.

Then you have the choice on how to remount it. If you are going to reuse the same holes in the head tube, cut off some of the threaded part of the screw so that it does not interfere with the steerer tube once the fork is installed. Also make sure the threaded part of the screw will fit through the head tube hole. Chances are it will but you will not be able to secure the headbage with the screws since they will be too small. Then insert the screws into the headbage and use a very small amount of two part epoxy on the back of the headbage to secure the screws. Be carefull the no epoxy squeezes through onto the front of the headbage. Also make sure that you do not build the epoxy up around the screw or the badge will not rest against the head tube. Let the epoxy cure. Use a small amount of silicone to mount the headbage.

Simple, but it takes some time. Good luck!