Considering the Dragon from the Hobbit (read the book / watch movie) was the only thing as hot as mount doom's Volcano - if any other Volcano in Middle earth or Furnace was equally as hot, then the movies would be very different.
Back on topic, considering the weapon from both Deathstars could pretty much turn a planet into dust and pebble - I'd dare say yes... it would VERY easily destroy the one ring. The Deathstar is more than a single 'super volcano' in terms of firepower.
Dragonfire could not destroy the One Ring. Dragonfire could destroy the other Rings of Power, but the One could only be destroyed in Mount Doom.