Electric > Water > Ground could be an idea, though it's a bit unfair for Electric not having any effect at all on Ground while Ground can attack Water without a drawback, from what I recall (might be wrong, haha).
Fighting > Dark > Psychic is actually the best trio I've heard of, apart from the standard element-inspired one. It's actually been used, with Greninja being Water/Dark, Delphox being Fire/Psychic and Chesnaught being Grass/Fighting. I do think they should have switched the typings around a bit on the pokémon species though, to make it a bit like in 4th gen. Torterra had a second type that could counter Infernape's fire, Infernape's Fighting type could hit Empoleon's Steel. Instead of making each pokémon extra weak to the one it's already weak against.