Drill the heads out without damaging the counter sink. Then trim the rivet to a length with an extra 3/4 (rule of thumb) of the rivet diameter than the width of the parts to be riveted together. Then whilst ensuring that the parts are held together and support the other head end of the rivet on the vice or something solid, pein over (with a ball pein hammer) the end of the rivet to fill the counter sink or create a dome head. A larger number of small taps rather than a few big hits, I used a metal plate to protect the fiber gear while I did the riveting. Finish this with a rivet set for a domed head if you have one, or file flush the counter sink.
Stu