  A quantitative description of Coulomb interactions is developed for
two-dimensional superconducting materials, enabling us to compare intrinsic
with external screening effects, such as those due to substrates. Using the
example of a doped monolayer of MoS2 embedded in a tunable dielectric
environment, we demonstrate that the influence of external screening is limited
to a length scale, bounded from below by the effective thickness of the
quasi-two-dimensional material and from above by its intrinsic screening
length. As a consequence, it is found that unconventional Coulomb-driven
superconductivity cannot be induced in MoS2 by tuning the substrate properties
alone. Our calculations of the retarded Morel-Anderson Coulomb potential {\mu
*} reveal that the Coulomb interactions, renormalized by the reduced layer
thickness and the substrate properties, can shift the onset of the
electron-phonon driven superconducting phase in monolayer MoS2 but do not
significantly affect the critical temperature at optimal doping.
