My Dad used to do a lot of bronze and brass work. One can braze a brass casting with O2acetylene torch, but the parent metal melts at the same temp as the filler rod.
We had best success by making our own brass rivets on the lathe, drilling a hole, peening them in, then filing them to smooth/blend. On small holes I would think you could use small solid brass nails, as long as they were solid brass. Be sure to add a countersink on the other side to lock it in place.