Bit of tin can just a bit wider than the balls to go round and have the end bent up at 90 degrees.
Insert springs with dab of grease or even super glue the lower coil into place, balls on the spring then wrap the band round and grip with a pair of snipe nosed pliers.
Offer the outer ring over pushing the band down to the bottom and then when you are sure some of the balls are inside the ring, remove tension from the pliers and unwrap the band.
Basically you have invented the piston ring clamp again, secret is getting it thin enough to hld the balls but slide down as the outer ring is going on.