  Binary neutron star (NS) mergers are among the most promising sources of
gravitational waves (GWs), as well as candidate progenitors for short Gamma-Ray
Bursts (SGRBs). Depending on the total initial mass of the system, and the NS
equation of state (EOS), the post-merger phase can see a prompt collapse to a
black hole, or the formation of a supramassive NS, or even a stable NS. In the
case of post-merger NS (PMNS) formation, magnetic field amplification during
the merger will produce a magnetar with a large induced mass quadrupole moment,
and millisecond spin. If the timescale for orthogonalization of the magnetic
symmetry axis with the spin axis is sufficiently short the NS will radiate its
spin down energy primarily via GWs. Here we study this scenario for various
outcomes of NS formation: we generalise the set of equilibrium states for a
twisted torus magnetic configuration to include solutions that, at a fixed
exterior dipole field, carry a larger magnetic energy reservoir; we hence
compute their magnetic ellipticity and the strength of the expected GW signal
as a function of the magnitude of the dipole and toroidal field. The relative
number of GW detections from PMNSs and from binary NSs is a strong function of
the NS equation of state (EOS), being higher (~ 1%) for the stiffest EOSs and
negligibly small for the softest ones. For intermediate-stiffness EOSs, such as
the n=4/7 polytrope recently used by Giacomazzo \& Perna or the GM1 used by
Lasky et al., the relative fraction is ~0.3%; correspondingly we estimate a GW
detection rate from stable PMNSs of ~ (0.1-1) yr$^{-1}$ with Advanced
detectors, and of ~ (100-1000) yr$^{-1}$ with third generation detectors such
as the Einstein Telescope. Measurement of such GW signal would provide strong
constraints on the NS EOS and on the nature of the binary progenitors giving
rise to SGRBs.
