  Neutron stars (NSs) in low-mass X-ray binaries rotate at frequencies high
enough to significantly deviate from sphericity ($\nu_* \sim$ 200--600 Hz). We
investigate the effects of rapid rotation on the observational appearance of a
NS. We propose analytical formulae relating gravitational mass and equatorial
radius of the rapidly rotating NS to the mass $M$ and radius $R$ of a
non-rotating NS of the same baryonic mass using accurate fully relativistic
computations. We compute spectra from an oblate rotating NS observed at
different inclination angles using the modified oblate Schwarzschild (MOS)
approximation, where light bending is computed in Schwarzschild metric, but
frame dragging and quadrupole moment of a NS are approximately accounted for in
the photon redshift calculations. We generalize the cooling tail method to the
case of a rapidly rotating NS to obtain the most probable values of $M$ and $R$
of the corresponding non-rotating NS with the same baryonic mass. We
approximate the local spectra from the NS surface by a diluted blackbody using
previously computed NS atmosphere models. We show that the NS radius could be
overestimated by 3--3.5 km for face-on stars of $R\approx 11$ km rotating at
$\nu_* =$ 700 Hz if the version of the cooling tail method for a non-rotating
NS is used. We apply the method to an X-ray burst observed from the NS rotating
at $\nu_* \approx$ 532 Hz in SAX J1810.8$-$2609. The resulting radius of the
non-rotating NS (assuming $M=1.5 M_\odot$) becomes $11.8\pm0.5$ km if it is
viewed at inclination i=60 deg and $R=11.2\pm0.5$ km for a face-on view, which
are smaller by 0.6 and 1.2 km than the radius obtained using standard cooling
tail method ignoring rotation. The corresponding equatorial radii of these
rapidly rotating NSs are 12.3$\pm 0.6$ km (for i=60 deg) and 11.6$\pm 0.6$\,km
(for i=0 deg).
