  We discuss conformal manifolds for conformal field theories with boundaries
or defects. Using conformal perturbation theory we derive constraints on
coefficients appearing in the boundary operator product expansion and
three-point functions that need to be satisfied for the existence of marginal
couplings. We present several explicit examples where we confirm that
$\beta$-functions vanish using a position space regularization, differential
regularization. Where possible, we confirm that our $\beta$-function results
agree with the existing literature.
