  Some modified theories of gravity are known to predict monopolar, in addition
to the usual quadrupolar and beyond, gravitational radiation in the form of
`breathing' modes. For the same reason that octupole and higher-multipole terms
often contribute negligibly to the overall wave strain, monopole terms tend to
dominate. We investigate both monopolar and quadrupolar continuous
gravitational radiation from neutron stars deformed through internal magnetic
stresses. We adopt the Parameterised-Post-Newtonian formalism to write down
equations describing the leading-order stellar properties in a
theory-independent way, and derive some exact solutions for stars with mixed
poloidal-toroidal magnetic fields. We then turn to the specific case of
scalar-tensor theories to demonstrate how observational upper limits on the
gravitational-wave luminosity of certain neutron stars may be used to place
constraints on modified gravity parameters, most notably the Eddington
parameter $\gamma$. For conservative, purely poloidal models with
characteristic field strength given by the spindown minimum, upper limits for
the Vela pulsar yield $1-\gamma \lesssim 4.2 \times 10^{-3}$. For models
containing a strong toroidal field housing $\sim 99\%$ of the internal magnetic
energy, we obtain the bound $1- \gamma \lesssim 8.0 \times 10^{-7}$. This
latter bound is an order of magnitude tighter than those obtained from current
Solar system experiments, though applies to the strong-field regime.
