If we are going to have a new type, Sound would be cool. But ...
Let's think for a moment about body, mind and soul. It could be argued that Fighting represents body and Psychic represents mind. So, how about something like a 'Life' type, representing the soul/essence of a being? This would balance the triangle if Life was strong against Psychic, but weak against Fighting.
Also, the Psychic-Fighting-Dark triangle is not really a triangle. It needs to work both ways. Fighting is weak to Psychic, Dark is weak to Fighting, Psychic is weak to Dark, when looked at the other way, Fighting is not very effective against Psychic, Dark is NVE against Fighting, and Psychic has no damn effect on Dark. Dark is immune to Psychic. Thus, the 'triangle' is flawed.
If Fairy is real, though, we need a Fairy/Dark vampire Pokemon, to represent Edward Cullen.
~Deadly