A cosmological model for gamma-ray bursts is explored in which the radiation is produced as a broadly beamed pair fireball along the rotation axis of an accreting black hole. The black hole may be a consequence of neutron star merger or neutron star-black hole merger, but for long complex bursts, it is more likely to come from the collapse of a single Wolf-Rayet star endowed with rotation ('failed' Type Ib supernova). The disk is geometrically thick and typically has a mass inside 100 km of several tenths of a solar mass. In the failed supernova case, the disk is fed for a longer period of time by the collapsing star. At its inner edge the disk is thick to its own neutrino emission and evolves on a viscous time scale of several seconds. In a region roughly 30 km across, interior to the accretion disk and along its axis of rotation, a pair fireball is generated by neutrino annihilation and electron-neutrino scattering which deposit approximately 10 exp 50 ergs/s.