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Under similar experimental conditions to our previous paper, the fluorescence lifetimes of the $A~$ states of C$3$-Ne and C$3$-Ar have been determined. The uncertainties in the measured lifetimes are estimated to be better than 10%. About 50 perpendicular bands and 11 parallel bands of the $A~-X~$ system of C$3$ were used to probe the fluorescence lifetimes of the Ne and Ar complexes. It is not possible to reduce the backing pressure while measuring lifetimes of the complexes; we therefore reduced the average pressure of the chamber to 1$-$2 $\times$ 10$\mathrm{<mrow\; data-mjx-texclass="ORD">-5</mrow>}$ torr by lowering the repetition rate. No sign of predissociation was found in either complex. Transitions to high vibrational levels of the $A~$ state of C$3$, above 4500 cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$, give weak laser-induced fluorescence signals, so that lifetime measurements are not possible for some of these bands. The lifetimes of the levels of the Ne complex lying below 4300 cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ are generally shorter than 300 ns, except for some levels with C-C stretch excitation. The lifetimes of the Ne complex behave quite similarly to those of C$3$. In contrast, the lifetimes of the Ar complex do not follow the vibrational dependence of the lifetimes of C$3$ and C$3$-Ne. We speculate that the complicated lifetime pattern observed in the Ar complex can be attributed to interactions with nearby triplet levels.