Assume that there are only well behaved functions as mass distributions, and there are no other forces except gravitation. Is it than possible to create an arrangement where a variation of a certain quantity (could be mass density or gravitational field or momentum) has a resonance?
A matter distribution with a sinsuoidally varying monopole or dipole moment will only produce variations in the gravitational field within the matter distribution. If the quadrupole (or a higher multipole moment) varies sinsuoidally, you will produce gravitational waves in a way very analogous to how electromagnetic waves are produced, with the amplitude differing by just a few numeric constants.
I wouldn't expect the back-reaction of the wave to amplify the variation that created the wave in the first place, though. Is this what you mean by 'a resonance'?