A long-standing question in active galactic nucleus (AGN) research is how the corona is heated up to produce X-ray radiation much stronger than that arising from the viscous heating within the corona. In this paper, we carry out detailed investigations of magnetic-reconnection heating to the corona, specifically, studying how the disc and corona are self-consistently coupled with the magnetic field, and how the emergent spectra depend on the fundamental parameters of AGN. It is shown that diverse spectral shapes and luminosities over a broad bandpass from optical to X-ray can be produced from the coupled disc and corona within a limited range of the black hole mass, accretion rate, and magnetic field strength. The relative strength of X-ray emission with respect to optical/ultraviolet (UV) depends on the strength of the magnetic field in the disc, which, together with accretion rate, determines the fraction of accretion energy transported and released in the corona. This refined disc-corona model is then applied to reproduce the broad-band spectral energy distributions (SEDs) of a sample of 20 bright local AGNs observed simultaneously in X-ray and optical/UV. We find that, in general, the overall observed broad-band SEDs can be reasonably reproduced, except for rather hard X-ray spectral shapes in some objects. The radiation pressure-dominant region, as previously predicted for the standard accretion disc in AGN, disappears for strong X-ray sources, revealing that AGN accretion discs are indeed commonly stable as observed. Our study suggests the disc-corona coupling model involving magnetic fields to be a promising approach for understanding the broad-band spectra of bright AGNs.