  We present a novel semi-coherent targeted search method for continuous
gravitational waves (CW) emitted by pulsars in binary systems. The method is
based on a custom optimization of the coherence time according to the orbital
parameters and their uncertainties, as provided by electromagnetic
observations. While rotating pulsars are expected to produce
quasi-monochromatic CWs in their reference frame, their orbital motion
introduces an additional modulation in the observer frame, alongside the one
due to the Earth's motion. As a result, the received signal is dispersed across
a frequency range and corrections, aimed at removing the orbital modulation,
are therefore required to achieve detection. However, Doppler corrections can,
in some cases, significantly vary within the uncertainties with which orbital
parameters are known. In order to optimally exploit the constraints drawn from
electromagnetic observations we implement a semi-coherent search, more robust
than fully coherent methods, in which the coherence time is evaluated for each
source taking into account uncertainties in its orbital parameters. This method
was tested and applied to a set of twelve targets from the ATNF catalogue. The
search identified a single outlier which astrophysical origin has been
confidently excluded. For the first time to our knowledge, we then set upper
limits on the signal strain from these 12 pulsars, the lowest being
$h_{UL}\sim1.06\cdot10^{-25}$ for PSR J1326-4728B.
