  The generalized post-Keplerian parametrization for compact binaries on
eccentric bound orbits is established at second post-Newtonian (2PN) order in a
class of massless scalar-tensor theories. This result is used to compute the
orbit-averaged flux of energy and angular momentum at Newtonian order, which
means relative 1PN order beyond the leading-order dipolar radiation of
scalar-tensor theories. The secular evolution of the orbital elements is then
computed at 1PN order. At leading order, the closed form "Peters and Mathews"
relation between the semi-major axis $a$ and the eccentricity $e$ is found to
be independent of any scalar-tensor parameter, and is given by $a \propto
e^{4/3}/(1-e^2)$. Finally, the waveform is obtained at Newtonian order in the
form of a spherical harmonic mode decomposition, extending to eccentric orbits
the results obtained in arXiv:2201.10924.
