Otherwise, you can simply join Madanach's side and let him run rampant throughout the city. Then find the nearest Arcane Enchanter, use a regular silver ring and add a fortify smithing enchantment, with the same magnitude, on it. Then rename the ring "Silver-Blood Family Ring". There. A legit copy of the ring and it will be identical in appearance and value. And this method is technically not even cheating. :)
Madanach's escape is such a wasted part of the game. I was hoping for a new Forsworn merchant, but all you get is the armor and a thanks. As someone mentioned above just recreate the ring using enchanting. It isn't unique (can't be disenchanted), neither is the armor.
Sadly much of the game feels unfinished. When I originally played a Breton I had more interest in helping the Forsworn retake the reach than giving it to the Imperials or Stormcloaks. I was very disappointed that freeing Madanach didn't give the option.
While still in the Dwemer halls with the forsworn, you recieve all your equipment and the forsworn armor. At this point you'll be talking to Madanach while his minions will run off through the door to the outside. You're supposed to follow them after madanach unlocks the door but if you start to fight him and kill him before he gets to the door, you can take the key from his body. (Note that all his buddies who had just gone through the door will almost immedietly return. I wasn't able to beat them in a straight fight so I just took the key and ran out the door.) Once outside the door you will get the conversation with Thonar where he will give you the ring as well. If you do what I did and don't kill his buddies before leaving the dwemer halls, its a little tricky because once the conversation starts the forsworn will come out the door and try to kill you. Luckily once that happens the conversation ends and you can quickly run past or hop over them and either run away, fight them in a more advantageous manner, or take the easy route and get them to follow you over a bridge and then force push them off to their deaths. (Another note, you get the ring as soon as you start the conversation so don't worry about not finishing it.)
A little late pbviously but, I just completed this mission (for the millionth time) and did exactly as the guide said to get both items. This best way to do it is to recieve the armour of the old gods, save, and keep talking to him to guarantee everyone is in markarth. The key is to have a strong enough weapon or have good skills in a skill tree, once everyone has left, you can sneak or not (best if you do), you must be quick and hit Madanach with your weapon and as long as it one shot kills him both sides will be your friend once you leave. But because you killed Madanach Thonar will initiate conversation as soon as you exit to Markarth. Quickly exit the conversation and you will get the ring and you will have already gotten the armour from inside. Now kill the guards or the forsworn group and no one will attack you back. I killed the forsworn and I got the armour, the ring and didn't lose anyone from Markarth besides Thonar.