It is difficult to discover pulsars via their gamma-ray emission because current instruments typically detect fewer than one photon per million rotations. This creates a significant computing challenge for isolated pulsars, where the typical parameter search space spans wide ranges in four dimensions. It is even more demanding when the pulsar is in a binary system, where the orbital motion introduces several additional unknown parameters. Building on earlier work by Pletsch & Clark (arXiv:1408.6962), we present optimal methods for such searches. These can also incorporate external constraints on the parameter space to be searched, for example, from optical observations of a presumed binary companion. The solution has two parts. The first is the construction of optimal search grids in parameter space via a parameter-space metric, for initial semicoherent searches and subsequent fully coherent follow-ups. The second is a method to demodulate and detect the periodic pulsations. These methods have different sensitivity properties than traditional radio searches for binary pulsars and might unveil new populations of pulsars.
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