  Cosmological models with a dynamical dark energy field typically lead to a
modified propagation of gravitational waves via an effectively time-varying
gravitational coupling $G(t)$. The local variation of this coupling between the
time of emission and detection can be probed with standard sirens. Here we
discuss the role that Lunar Laser Ranging (LLR) and binary pulsar constraints
play in the prospects of constraining $G(t)$ with standard sirens. In
particular, we argue that LLR constrains the matter-matter gravitational
coupling $G_N(t)$, whereas binary pulsars and standard sirens constrain the
quadratic kinetic gravity self-interaction $G_{gw}(t)$. Generically, these two
couplings could be different in alternative cosmological models, in which case
LLR constraints are irrelevant for standard sirens. We use the Hulse-Taylor
pulsar data and show that observations are highly insensitive to time
variations of $G_{gw}(t)$ yet highly sensitive to $G_N(t)$. We thus conclude
that future gravitational waves data will become the best probe to test
$G_{gw}(t)$, and will hence provide novel constraints on dynamical dark energy
models.
