  We use the weak coupling renormalization group method to examine the
interplay between charge-density-wave and s-wave superconducting orders in a
quasi-one-dimensional model of electrons interacting with acoustic phonons. The
relative stability of both types of order is mapped out at arbitrary nesting
deviations and Debye phonon frequency $\omega_D$. We singled out a power law
increase of the superconducting $T_c\sim \omega_D^{0.7}$ from a quantum
critical point of charge-density-wave order triggered by nesting alterations.
The results capture the key features shown by the proximity between the two
types of ordering in the phase diagram of the recently discovered Perylene
based organic superconductor under pressure. The impact of Coulomb interaction
on the relative stability of the competing phases is examined and discussed in
connection with the occurrence of s-wave superconductivity in low dimensional
charge-density-wave materials.
