The spectrum of meson and diquark excitations of dense color neutral cold quark matter is investigated in the framework of a two-flavored Nambu--Jona-Lasinio--type model, including a quark $\ensuremath{\mu}$- and color ${\ensuremath{\mu}}_{8}$-chemical potential. It was found that, in the color superconducting (2SC) phase, i.e. at $\ensuremath{\mu}>{\ensuremath{\mu}}_{c}=342\text{ }\text{ }\mathrm{MeV}$, ${\ensuremath{\mu}}_{8}$ acquires rather small values $\ensuremath{\sim}10\text{ }\text{ }\mathrm{MeV}$ in order to ensure the color neutrality. In this phase the $\ensuremath{\pi}$ and $\ensuremath{\sigma}$ meson masses are evaluated around $\ensuremath{\sim}330\text{ }\text{ }\mathrm{MeV}$. The spectrum of scalar diquarks in the color neutral 2SC phase consists of a heavy [${\mathrm{SU}}_{c}(2)$-singlet] resonance with mass $\ensuremath{\sim}1100\text{ }\text{ }\mathrm{MeV}$, four light diquarks with mass $3|{\ensuremath{\mu}}_{8}|$, and one Nambu-Goldstone boson, which is in accordance with the Goldstone theorem. Moreover, in the 2SC phase there are five light stable particles as well as a heavy resonance in the spectrum of pseudoscalar diquarks. In the color symmetric phase, i.e. for $\ensuremath{\mu}<{\ensuremath{\mu}}_{c}$, a mass splitting of scalar diquarks and antidiquarks is shown to arise if $\ensuremath{\mu}\ensuremath{\ne}0$, contrary to the case of $\ensuremath{\mu}=0$, where the masses of scalar antidiquarks and diquarks are degenerate at the value $\ensuremath{\sim}700\text{ }\text{ }\mathrm{MeV}$. If the coupling strength in the pseudoscalar diquark channel is the same as in the scalar diquark one (as for QCD-inspired Nambu--Jona-Lasinio models), then in the color symmetric phase pseudoscalar diquarks are not allowed to exist as stable particles.