n-dimensional coherent states systems generated by translations, modulations, rotations and dilations are described. Starting from unitary irreducible representations of the n-dimensional affine Weyl-Heisenberg group, which are not square-integrable, one is led to consider systems of coherent states labeled by the elements of quotients of the original group. Such systems can yield a resolution of the identity, and then be used as alternatives to usual wavelet or windowed Fourier analysis. When the quotient space is the phase space of the representation, different embeddings of it into the group provide different descriptions of the phase space.