If you had both Nicol Bolas (the creature) and Rings of Brighthearth out and then swung with Bolas, would you be able to copy the discard effect of Bolas with the rings to a new target? Or would you only be able to copy it to the same person? Also, would you be able to copy it at all?
Nicol Bolas's triggered ability does not have a target (because it doesn't say "target" anywhere). If you copy the ability with Strionic Resonator, the same player will discard their hand again. You can't copy the ability with Rings of Brighthearth because that copies activated abilities.
This won't work. Rings of Brighthearth can only copy activated abilities and Nicol Bolas 's discard ability is a triggered one. In addition if you did copy it with say Strionic Resonator it would only effect the same player as it doesn't target so you cannot change any targets.
Rings of Brighthearth + Nicol Bolas