While much effort in Stirling engine development is placed on making the high-temperature region of the Stirling engine warmer, this research explores methods to lower the temperature of the cold region by improving heat transfer in the cooler. This paper presents heat transfer coefficients obtained for a Stirling engine heat exchanger with oscillatory flow. The effects of oscillating frequency and input heat rate on the heat transfer coefficients are evaluated and details on the design and development of the heat exchanger test apparatus are also explained. Featured results include the relationship between overall heat transfer coefficients and oscillation frequency which increase from 21.5 to 46.1 Wm-2K-1 as the oscillation frequency increases from 6.0 to 19.3 Hz. A correlation for the Nusselt number on the inside of the heat exchange tubes in oscillatory flow is presented in a concise, dimensionless form in terms of the kinetic Reynolds number as a result of a statistical analysis. The test apparatus design is proven to be successful throughout its implementation due to the usefulness of data and clear trends observed. The author is not aware of any other publicly-available research on a Stirling engine cooler to the extent presented in this paper. Therefore, the present results are analyzed on a part-by-part basis and compared to segments of other research; however, strong correlations with data from other studies are not expected. The data presented in this paper are part of a continuing effort to better understand heat transfer properties in Stirling engines as well as other oscillating flow applications.