They haven't displayed any other combos of rings having power over one another, but any combination of different colors allows for the defeat of a Black Lantern.
Alan found the Starheart when it landed on Earth and carved a ring and a battery from it, and later internalized its powers. His power is born of the univere's magic, unrelated to the Corps and as such, he doesn't draw from the Central Power Battery or necessarily even from the emotional spectrum.
Kyle's first stint as Ion began when he absorbed the energy Parallax (Hal) left in the sun when he gave his life to defeat the Sun-Eater. He used this power as the near-omnipotent Ion for a time, but gave it up when he realized that the power was the essence of the Guardians of the Universe that Hal had murdered when he stormed Oa. He deposited the energy in the Central Battery on Oa, birthing new, baby Guardians; the current Guardians of the Universe are the grown forms of those baby Guardians. He returned to his status as a normal Green Lantern (though not before making some modifications to his ring, like an emergency energy charge and the ability to return to him if it were removed from his finger) and continued to operate as that for a time.
His second stint as Ion began when Jade was killed in the Rann-Thanagar conflict. She gave what was left of her energy to Kyle before she died, and he became Ion once again. He operated as Ion until the Sinestro Corps War, when Sinestro revealed that "Ion" was in fact the embodiment of willpower and a sentient being of energy, residing within Kyle. Sinestro forcibly removed Ion from Kyle and allowed the Parallax entity - to fear, what Ion is to willpower - to possess Kyle.
So "Ion" is really just one giant ball of green willpower energy that manifests as a green whale and can be placed within an individual so that they may use its power. Sodam Yat was made the new Ion near the end of the Sinestro Corps conflict when the Guardians placed the entity within him.