We study covert communications over binary-input discrete memoryless alarm two-way channels, in which two users interact through a two-way channel and attempt to hide the presence of their communication from an eavesdropping receiver. The alarm two-way channel is one in which simultaneous transmissions by both users trigger an alarm at the eavesdropper, which captures the challenges and opportunities of cooperation beyond interference management. In particular, by characterizing the covert capacity region of two-way channels when using public time sharing, we show how cooperation strictly improves achievable covert communication throughputs. While our analysis falls short of characterizing the two-way covert capacity region for all two-way channels, we provide general achievable and converse bounds that illuminate the cooperation mechanisms that benefit covertness and are tight for a physically-degraded alarm two-way channels. Because of the unique nature of covert communications, our analysis also shows that the coordination required to avoid triggering alarms comes asymptotically "for free". The key technical challenge that we address is how to appropriately design auxiliary random variables in a multi-user covert communication setting subject to the square root law.