  I derive a formula for the coupling-constant derivative of the coefficients
of the operator product expansion (Wilson OPE coefficients) in an arbitrary
curved space, as the natural extension of the quantum action principle.
Expanding the coefficients themselves in powers of the coupling constants, this
formula allows to compute them recursively to arbitrary order. As input, only
the OPE coefficients in the free theory are needed, which are easily obtained
using Wick's theorem. I illustrate the method by computing the OPE of two
scalars $\phi$ in hyperbolic space (Euclidean Anti-de Sitter space) up to terms
vanishing faster than the square of their separation to first order in the
quartic interaction $g \phi^4$, as well as the OPE coefficient
$\mathcal{C}^{\mathbb{1}}_{\phi \phi}$ at second order in $g$.
