  We derive a universal formula for the average heavy-heavy-light structure
constants for 2d CFTs with non-vanishing u(1) charge. The derivation utilizes
the modular properties of one-point functions on the torus. Refinements in N=2
SCFTs, show that the resulting Cardy-like formula for the structure constants
has precisely the same shifts in the central charge as that of the
thermodynamic entropy found earlier. This analysis generalizes the recent
results by Kraus and Maloney for CFTs with an additional global u(1) symmetry.
Our results at large central charge are also shown to match with computations
from the holographic dual, which suggest that the averaged CFT three-point
coefficient also serves as an useful probe of detecting black hole hair.
