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Near-infrared CO molecular lines are suggested to be linked with dynamic processes in post-AGB stars; however, they have not been investigated at high spectral resolution. CO second overtone line variability in the H-band is presented for the cool carbon-rich post-AGB stars IRAS 22272+5435, IRAS Z02229+6208, and IRAS 20000+3239. CO features are observed to change intensity, shape, and radial velocity as well as switch between emission and absorption during the pulsation cycle. At all times, the CO line positions are located no more than around 10 km/s away from the systemic velocity. Molecular line variation is qualitatively similar in all three stars, and it appears that the site of formation is the extended atmosphere. Emission in CO lines tends to be strongest during pulsation phases close to light maximum, and weakest emission or absorption tends to be seen when close to light minimum, resembling the behaviour in CN Red and C$_2$ Swan system lines at shorter wavelengths. The connection of molecular line variability with pulsation of the star could be related to a shock that traverses the atmosphere once per pulsation cycle.