  Neutron stars in low mass X-ray binaries are hypothesised to emit continuous
gravitational waves that may be detectable by ground-based observatories. The
torque balance model predicts that a higher accretion rate produces
larger-amplitude gravitational waves, hence low mass X-ray binaries with high
X-ray flux are promising targets for gravitational wave searches. The detection
of X-ray pulsations would identify the spin frequency of these neutron stars,
and thereby improve the sensitivity of continuous gravitational-wave searches
by reducing the volume of the search parameter space. We perform a
semi-coherent search for pulsations in the two low mass X-ray binaries Scorpius
X-1 and Cygnus X-2 using X-ray data from the \textit{ Rossi X-ray Timing
Explorer} Proportional Counter Array. We find no clear evidence for pulsations,
and obtain upper limits (at $90\%$ confidence) on the fractional pulse
amplitude, with the most stringent being $0.034\%$ for Scorpius X-1 and
$0.23\%$ for Cygnus X-2. These upper limits improve upon those of Vaughan et
al. (1994) by factors of $\sim 8.2$ and $\sim 1.6$ respectively.
