Yes, there are weapons which have a special effect, like "Consumes 25% less AP in V.A.T.S Mode". However, these weapons are only obtainable from legendary enemies.
In my experience, the AP cost of a weapon are determined by the following things:
- Weapon mods which start with light (less AP cost) or heavy (more AP cost)
- Fire rate (higher fire rate needs more AP)
- Sights (Scope needs more AP, while reflex needs less AP)
- Stock type (Short stock needs less AP)
- Accuracy (the more accurate a weapon is, the more AP it needs)
Against contrary believe, the weight of a weapon does NOT affect the AP usage of it.