This paper studies frequent-offer limits of perfect Bayesian equilibria in the alternating-offer bilateral bargaining model with private correlated values. The correlation of values is modeled via the global games information structure: values depend on the unobserved quality of the object and idiosyncratic factors. For any level of correlation we construct a punishing path that exhibits the Coasian dynamics and enables to sustain a variety of outcomes even when the correlation of values is almost perfect. We characterize the Pareto frontier of frequent-offer PBE limits as the correlation approaches perfect and show that such limits exhibit no delay, but the surplus split generally differs from that in the complete-information game. We also construct frequent-offer PBE limits that exhibit trade delays even when the correlation of values is close to perfect. Our findings highlight the role of public information for bargaining delays.