We investigate cooperative in-band radar and communications signaling for frequency-modulated continuous-wave (FMCW) radar and Doppler estimation. While each system typically considers the other system a source of interference, by considering the radar and communications operations to be a single system, joint performance bounds can be formulated. We extend previous work where a novel estimation and information theoretic bound formulation was constructed for a receiver that observes communications and radar returns in the same frequency allocation. While the previous work derived a joint performance bound in terms of the communications rate and the target delay estimation rate of the system for pulsed waveforms, we derive a similar bound for FMCW radar and include Doppler estimation. This extension is important given the rise of popularity of FMCW radars, and since the continuous signaling brings them closer to how communications systems operate.