We describe the results of an efficient survey to identify bright B < ∼ 18 active galactic nuclei (AGN) within ≈ 4 • (4.7 h −1 Mpc projected radius) of the centre of the Coma cluster of galaxies. The candidates have been carefully selected either as unresolved UV-excess objects with no detected proper motion, or from identifications on objective-prism plates including a few ROSAT sources. A global success rate larger than 30% is achieved. Low-resolution spectra are presented for the extragalactic objects identified in the course of the survey: the sample contains 16 emission-line objects, a BL Lac candidate and an elliptical galaxy. The AGNs of this list are unique targets to study the association of the Lyman-α forest with large-scale structures and galactic haloes at low redshift, to search for warm gas within the Coma cluster and nearby filaments, and for optical monitoring to detect the micro-lensing variability produced by the baryonic dark matter in the cluster.