Magnetic buoyancy (MBI) and Parker instabilities are strong, generic instabilities expected to occur in most astrophysical systems with sufficiently strong magnetic fields. In galactic and accretion discs, large-scale magnetic fields are thought to arise from mean-field dynamo action, particularly the -dynamo. Using non-ideal MHD equations, we model a section of the galactic disc where the large-scale magnetic field is generated by an imposed -effect and differential rotation. We extend our previous study of the interplay between magnetic buoyancy and the mean-field dynamo by incorporating differential rotation, which enhances the dynamo, and cosmic rays, which amplify magnetic buoyancy. We construct a simple one-dimensional (1D) model which replicates all significant features of the three-dimensional (3D) simulations. Simulations confirm that magnetic buoyancy can lead to oscillatory magnetic fields and reveal that it can change the magnetic field parity between quadrupolar and dipolar states. Differential rotation facilitates this switch in parity, suggesting that the large-scale magnetic field can adopt a dipolar parity within a few kiloparsecs of the galactic centre. In contrast, quadrupolar parity may remain predominant in the outer parts of a galactic disc. Cosmic rays accelerate both the dynamo and the MBI, supporting oscillatory non-linear states and a spatial magnetic field structure similar to the alternating magnetic field directions observed in the haloes of some edge-on galaxies.