In this paper, we present the first results of radiative transfer calculations on decretion discs of binary Be stars. A smoothed particle hydrodynamics code computes the structure of Be discs in coplanar circular binary systems for a range of orbital and disc parameters. The resulting disc configuration consists of two spiral arms, and this can be given as input into a Monte Carlo code, which calculates the radiative transfer along the line of sight for various observational coordinates. Making use of the property of steady disc structure in coplanar circular binaries, observables are computed as functions of the orbital phase. Some orbital-phase series of line profiles are given for selected parameter sets under various viewing angles, to allow comparison with observations. Flat-topped profiles with and without superimposed multiple structures are reproduced, showing, for example, that triple-peaked profiles do not have to be necessarily associated with warped discs and misaligned binaries. It is demonstrated that binary tidal effects give rise to phase-locked variability of the violet-to-red (V/R) ratio of hydrogen emission lines. The V/R ratio exhibits two maxima per cycle; in certain cases those maxima are equal, leading to a clear new V/R cycle every half orbital period. This study opens a way to identifying binaries and to constraining the parameters of binary systems that exhibit phase-locked variations induced by tidal interaction with a companion star.