If they are standard you can get them from industrial hardware distributors.
If they are not standard you can cut a pins out of your preferred material, then put the pin in the place and swage the ends ultrasonicaly.
You can contact me if you need more help.

Tank you vahanyan I am glad to see your mesage and my apoligase for my english, becouse I am in Europe. I wold make not standard rivet in my company and we make tool for rubber. I would be wery takfuul if You send me some adres of good produser.
Best regardes

Hello sretas.
Are you looking for rivet vendor or you're looking a vendor for special machine?
Please clearify.

Vahanyan,
I am lookinkg for rivet vendor. My job is design machines and I will aply this rivet, but when I loking for this stuff we start interest for manufacturing some rivet for us. We are producer of equipment and machines for wire and cable industry.
Tank you mu friend

Please send me a rough sketch or dimensions of the rivets you're looking for. I will look around for you and get the best answer. Also you can contact me at hvahanyan@1ams.com
Thanks

   
  Hi There,
            We manufacture different type's of Rivet's
 here in UK and if you wish to send to me at the
 following e-mail stating QTY'S and I will give you a
 Prompt reply if we can Help.
              Regard's
                      James
    E-Mail...  sbrady1@gofree.indigo.ie

As you know, metal rivets are installed in the hole then upset (hot or cold forged) to hold them in place and to hold the parts together.

Elastomeric rivets must be installed the same way. The most suitable material from which to make the rivet depends upon the total of the thicknesses of the materials to be joined (the grip of th rivet), the loading conditions (stress, vibration, cycling, etc), and the environment (chemical, thermal, etc). There are many "thermoplastic" plastics which might be considered for this application. A "thermoplastic" plastic, as opposed to a "thermosetting" plastic is one which can be remelted and reset thermally.

If you provide a few more details regarding your application, someone can probably give you more specific recommendations about what worked for them in similar situations.

Best of luck.