  We carried out a comprehensive study of the electronic, magnetic, and
thermodynamic properties of Ni-doped ZrTe$_2$. High quality
Ni$_{0.04}$ZrTe$_{1.89}$ single crystals show a possible coexistence of charge
density waves (CDW, T$_{CDW}\approx287$\,K) with superconductivity (T$_c\approx
4.1$\,K), which we report here for the first time. The temperature dependence
of the lower (H$_{c_1}$) and upper (H$_{c_2}$) critical magnetic fields both
deviate significantly from the behaviors expected in conventional single-gap
s-wave superconductors. However, the behaviors of the normalized superfluid
density $\rho_s(T)$ and H$_{c_2}(T)$ can be described well using a two-gap
model for the Fermi surface, in a manner consistent with conventional multiband
superconductivity. Electrical resistivity and specific heat measurements show
clear anomalies centered near 287\,K consistent with a CDW phase transition.
Additionally, electronic-structure calculations support the coexistence of
electron-phonon multiband superconductivity and CDW order due to the
compensated disconnected nature of the electron- and hole-pockets at the Fermi
surface. Our electronic structure calculations also suggest that ZrTe$_2$ could
reach a non-trivial topological type-II Dirac semimetallic state. These
findings highlight that Ni-doped ZrTe2 can be uniquely important for probing
the coexistence of superconducting and CDW ground states in an electronic
system with non-trivial topology.
