Aims. The detection of c-C3HC2H and possible future detection of c-C3HCN provide new molecules for reaction chemistry in the dense interstellar medium (ISM) where R-C2H and R-CN species are prevalent. Determination of chemically viable c-C3HC2H and c-C3HCN derivatives and their prominent spectral features can accelerate potential astrophysical detection of this chemical family. This work characterizes three such derivatives: c-C-3(C2H)(2), c-C-3(CN)(2), and c-C-3(C2H)(CN). Methods. Interstellar reaction pathways of small carbonaceous species are well replicated through quantum chemical means. Highly accurate cc-pVXZ-F12/CCSD(T)-F12 (X = D,T) calculations generate the energetics of chemical formation pathways as well as the basis for quartic force field and second-order vibrational perturbation theory rovibrational analysis of the vibrational frequencies and rotational constants of the molecules under study. Results. The formation of c-C-3(C2H)(2) is as thermodynamically and, likely, as stepwise favorable as the formation of c-C3HC2H, rendering its detectability to be mostly dependent on the concentrations of the reactants. Both c-C-3(C2H)(2) and c-C-3(C2H)(CN) will be detectable through radioastronomical observation with large dipole moments of 2.84 D and 4.26 D, respectively, while c-C-3(CN)(2) has an exceedingly small and likely unobservable dipole moment of 0.08 D. The most intense frequency for c-C-3(C2H)(2) is nu(2) at 3316.9 cm(-1) (3.01 mu m), with an intensity of 140 km mol(-1). The mixed-substituent molecule c-C-3(C2H)(CN) has one frequency with a large intensity,nu(1), at 3321.0 cm(-1) (3.01 mu m), with an intensity of 82 km mol(-1). The molecule c-C-3(CN)(2) lacks intense vibrational frequencies within the range that current instrumentation can readily observe. Conclusions. Both c-C-3(C2H)(2) and c-C-3(C2H)(CN) are viable candidates for astrophysical observation, with favorable reaction profiles and spectral data produced herein, but c-C-3(CN)(2) will not be directly observable through any currently available remote sensing means, even if it forms in large abundances.