  Operators with integer scaling dimensions in even-dimensional conformal field
theories exhibit well-known type-B Weyl anomalies. In general, these anomalies
depend non-trivially on exactly marginal couplings. We study the corresponding
fully covariantised anomaly functional on conformal manifolds in several
examples. We show that a natural consequence of the Wess-Zumino consistency
condition is that the anomalies are covariantly constant with respect to the
exactly marginal couplings. The argument is general and applies even when the
conformal symmetry is spontaneously broken on moduli spaces of vacua.
