We present a new type of search strategy designed specifically to find continuously emitting gravitational wave sources in known binary systems. A component of this strategy is based on the incoherent summation of frequency-modulated binary signal sidebands, a method previously employed in the detection of electromagnetic pulsar signals from radio observations. The search pipeline can be divided into three stages: the first is a wide bandwidth, -statistic search demodulated for sky position. This is followed by a fast second stage in which areas in frequency space are identified as signal candidates through the frequency domain convolution of the -statistic with an approximate signal template. For this second stage only precise information on the orbit period and approximate information on the orbital semi-major axis are required a priori. For the final stage we propose a fully coherent Markov chain Monte Carlo based follow-up search on the frequency subspace defined by the candidates identified by the second stage. This search is particularly suited to the low-mass x-ray binaries, for which orbital period and sky position are typically well known and additional orbital parameters and neutron star spin frequency are not. We note that for the accreting x-ray millisecond pulsars, for which spin frequency and orbital parameters are well known, the second stage can be omitted and the fully coherent search stage can be performed. We describe the search pipeline with respect to its application to a simplified phase model and derive the corresponding sensitivity of the search.