Annular quasimonoenergetic electron beams with a mean energy in the range 200-400 MeV and charge on the order of several picocoulombs were generated in a laser wakefield accelerator and subsequently accelerated using a plasma afterburner in a two-stage gas cell. Generation of these beams is associated with injection occurring on the density down ramp between the stages. This well-localized injection produces a bunch of electrons performing coherent betatron oscillations in the wakefield, resulting in a significant increase in the x-ray yield. Annular electron distributions are detected in 40% of shots under optimal conditions. Simultaneous control of the pulse duration and frequency chirp enables optimization of both the energy and the energy spread of the annular beam and boosts the radiant energy per unit charge by almost an order of magnitude. These well-defined annular distributions of electrons are a promising source of high-brightness laser plasma-based x rays.