I accidentally hit Sinding with fire while trying to kill the hunters for the Ring then was going to go back in and skin him. But after accidentally hitting him, he is attacking me. All of the hunters are dead and both Speak with Sinding and Kill Sinding showed up on the screen after killing the last hunter. What do I do to be able to let him live?
There are multiple things to try.
Exit the area. It is possible that the aspect of Hircine will show up, and you can automatically advance to the next part of the quest.
Exit the area, wait for 24 hours, reenter and talk to Sinding. Most NPCs calm down after a while.
Cast a calm spell. The illusion school has many calm spells. You can buy them from Drevis in the College of Winterhold. If you are an imperial, you can use Voice of the Emperor. It is also possible that the Kyne's peace shout will calm Sinding.
I found out that you can get both Ring of Hircine and Savior's Hide. You said you accidentaly attacked Sinding while killing the hunters. Just kill him, take his skin, then when the spirit appears, don't talk to it, instead go back to the entrance where Hircine will give you the Ring. Then go back to the spirit of Sinding and get the Savior's Hide.
NOTE: Since you want to let him live and not get both items, use a calm spell or power, otherwise go to cheats if you're on PC and click on Sinding and type