In this work, we study the trade-off between the cache capacity and the user delay for a cooperative Small Base Station (SBS) coded caching system with mobile users. First, a delay-aware coded caching policy, which takes into account the popularity of the files and the maximum re-buffering delay to minimize the average rebuffering delay of a mobile user under a given cache capacity constraint is introduced. Subsequently, we address a scenario where some files are served by the macro-cell base station (MBS) when the cache capacity of the SBSs is not sufficient to store all the files in the library. For this scenario, we develop a coded caching policy that minimizes the average amount of data served by the MBS under an average re-buffering delay constraint.