We discuss methods to determine L-M-N coordinate systems for current sheet crossings observed by the Magnetospheric Multiscale (MMS) spacecraft mission during ongoing reconnection, where e(L) is the direction of the reconnecting component of the magnetic field, B, and e(N) is normal to the magnetopause. We present and test a new hybrid method, with e(L) estimated as the maximum variance direction of B (MVAB) and e(N) as the direction of maximum directional derivative of B, and then adjust these directions to be perpendicular. In the best case, only small adjustment is needed. Results from this method, applied to an MMS crossing of the dayside magnetopause at 1305:45UT on 16 October 2015, are discussed and compared with those from other methods for which e(N) is obtained by other means. Each of the other evaluations can be combined with e(L) from MVAB in a generalized hybrid approach to provide an L-M-N system. The quality of the results is judged by eigenvalue ratios, constancy of directions using different data segments and methods, and expected sign and magnitude of the normal component of B. For this event, the hybrid method appears to produce e(N) accurate to within less than 10 degrees. We discuss variance analysis using the electric current density, J, or the J x B force, which yield promising results, and minimum Faraday residue analysis and MVAB alone, which can be useful for other events. We also briefly discuss results from our hybrid method and MVAB alone for a few other MMS reconnection events. Plain Language Summary We discuss methods for determining coordinate systems in order to study magnetic reconnection events at the magnetopause, the boundary between the ionized gas in the region of space dominated by the Earth's magnetic field and the ionized gas coming from the solar wind. We introduce a new method that combines results from multiple methods in order to determine the three coordinate directions in space. We demonstrate this method by applying it to an event observed by the Magnetospheric Multiscale spacecraft on 16 October 2015 and at other times.