Highly coherent and powerful light sources capable of generating soft x-ray frequency combs are essential for high precision measurements and rigorous tests of fundamental physics. In this work, we derive the analytical conditions required for the emission of coherent radiation from an electron beam colliding with a laser pulse, modeled as a plane wave. These conditions are applied in a series of numerical simulations, where we show that a soft x-ray frequency comb can be produced if the electrons are regularly-spaced and sufficiently monoenergetic. High quality beams of this kind may be produced in the near future from laser-plasma interactions or linear accelerators. Furthermore, we highlight the advantageous role of employing few-cycle laser pulses in relaxing the stringent monoenergeticity requirements for coherent emission. The conditions derived here can also be used to optimize coherent emission in other frequency ranges, such as the terahertz domain.