You'll need to get the right ones like the one's Lucky has, that backplate takes a pounding and those two rivets are crucial to keep the sideplates squeezed tightly on the backplate.
As an alternative, get two 3/16" allen head cap screws from Ace Hardware because they have a flat head and will seat against the inside of the top plate. Get the long ones where the threads stop and you have an unthreaded portion at least 3/4" long and cut them off to the correct length. Take a grinder to the allen head and dress it down until it fits inside the top plate. Don't get the Grade 8 cap screws, get the softer ones if available so they will park nicely.
Other types of screws will work too, but most other types in that small size are threaded all the way to the head and those threads may make for a funky looking domed rivet. Besides, with the threading you lose quite a bit of the diameter and shear resistence.