Single crystals of Ca(Co1-xIrx)(2-y)As-2 with 0 <= x <= 0.35 and 0.10 <= y <= 0.14 have been grown using the self-flux technique and characterized by single-crystal x-ray diffraction (XRD), energy-dispersive x-ray spectroscopy, magnetization M, and magnetic susceptibility chi measurements versus temperature T, magnetic field H, and time t, and heat-capacity C-p(H, T) measurements. The XRD refinements reveal that all the Ir-substituted crystals crystallize in a collapsed-tetragonal structure as does the parent CaCo2-yAs2 compound. A small 3.3% Ir substitution for Co in CaCo1.86As2 drastically lowers the A-type antiferromagnetic (AFM) transition temperature T-N from 52 to 23 K with a significant enhancement of the Sommerfeld electronic heat-capacity coefficient. The A-type AFM structure consists of ab-plane layers of spins ferromagnetically aligned along the c axis with AFM alignment of the spins in adjacent layers along this axis. The positive Weiss temperatures obtained from Curie-Weiss fits to the chi (T > T-N) data indicate that the dominant magnetic interactions are ferromagnetic (FM) for all x. A magnetic phase boundary is inferred to be present between x = 0.14 and x = 0.17 from a discontinuity in the x dependencies of the effective moment and Weiss temperature in the Curie-Weiss fits. FM fluctuations that strongly increase with increasing x are also revealed from the chi (T) data. The magnetic ground state for x >= 0.17 is a spin glass as indicated by hysteresis in chi(T) between field-cooled and zero-field-cooled measurements and from the relaxation of M in a small field that exhibits a stretched-exponential time dependence. The spin glass has a small FM component to the ordering and is hence inferred to be comprised of small FM clusters. The competing AFM and FM interactions along with crystallographic disorder associated with Ir substitution are inferred to be responsible for the development of a FM cluster-glass phase. A logarithmic T dependence of C-p at low T for x = 0.14 is consistent with the presence of significant FM quantum fluctuations. This composition is near the T = 0 boundary at x approximate to 0.16 between the A-type AFM phase containing ferromagnetically-aligned layers of spins and the FM cluster-glass phase.