If it is like mine were, there is a plastic center 'rod" which is pushed in to expand the rivet and hold it in place. There are three alternatives:

(1) Pry the rivet out a little bit carefully with a thin blade, push it in, and hope the rod/dowel then sticks-out enough that you can grab it with a small pliers and pull it back. The rivet should then con out.

(2) Use a finish type nail of the right diameter and carefully tap the dowel all the way through, using the blunt end of the nail against the center rod/dowel. You should then be able to pry the nail out, or use a screw to first screw in a couple of threads in the resultant hole, and pull it out.

(3) Carefully drill it out with a drill the diameter of the rod/dowel.

That's the technique I used, and should work for you if the rivets are the same.