Lynn, in response to your question, riveting of this type is done with a pneumatic hammer and what is called a bucking bar. On the hammer side is an attachment that forms the head and the bucking bar has the opposite head form shape. The process is done either cold or hot . This technology is very old, steam locomotives, structural steel, boilers etc. all being done this way. You can still get the tools for the job, but may have to get in contact with a boiler maker or a good machinist whol can fabricate the tools. A small pneumatic hammer is probably sufficient for the job since carrier rivets are comparatively small. It is a two man job, one for the hammer and one for the bucking bar. Wear your ear plugs.
