The time-window for processing electron spin information (spintronics) in solid-state quantum electronic devices is determined by the spin-lattice and spin-spin relaxation times of electrons. Minimizing the effects of spin-orbit coupling and the local magnetic contributions of neighbouring atoms on spin-lattice and spin-spin relaxation times at room temperature remain substantial challenges to practical spintronics. Here we report conduction electron spin-lattice and spin-spin relaxation times of 175 ns at 300 K in 37 +/- 7 nm carbon spheres, which is remarkably long for any conducting solid-state material of comparable size. Following the observation of spin polarization by electron spin resonance, we control the quantum state of the electron spin by applying short bursts of an oscillating magnetic field and observe coherent oscillations of the spin state. These results demonstrate the feasibility of operating electron spins in conducting carbon nanospheres as quantum bits at room temperature.