With an eyelet riveting pliers and the spring threaded over the setting post. Compress the spring to remove the completed assembly. Your only remaining problem is sourcing eyelets and pliers that closely match the spring's fixing eye diameter.
Worst case: you may have to make your own solid copper rivets. Drill a small pilot hole right through a block of steel. Redrill to the rivet diameter and to depth for the desired length. Polish the bore carefully and chamfer the edge slightly. Cut a piece of annealed pure copper rod of matching diameter to protrude from the hole no more than one diameter, lubricate it so it can be extracted, insert and peen to form the head. Punch the formed rivets out through the pilot hole. They *MUST* be re-annealed before use, and will need to be tumble-polished or wire-brushed to remove copper oxide if you want them to be solderable. You'll also need a setting anvil - take a steel rod that just fits through the end turn of the spring and drill or grind a dimple in the end to accommodate the peened rivet heads. Clamp firmly in a vice , assemble the rivet and spring on the anvil rod, hold the plate in place and peen the other end of the rivet to set it.