  We compute one-loop matter amplitudes in homogeneous Maxwell-Einstein
supergravities with N=2 supersymmetry using the double-copy construction. We
start from amplitudes of N=2 super-Yang-Mills theory with matter that obey
manifestly the duality between color and kinematics. Taking advantage of the
fact that amplitudes with external hypermultiplets have kinematical numerators
which do not present any explicit dependence on the loop momentum, we find a
relation between the one-loop divergence of the supergravity amplitudes and the
beta function of the non-supersymmetric gauge theory entering the construction.
Two distinct linearized counterterms are generated at one loop. The divergence
corresponding to the first is nonzero for all homogeneous supergravities, while
the divergence associated to the second vanishes only in the case of the four
Magical supergravities.
