Resistivity, susceptibility, and specific heat measurements on the new layered superconductors ${\mathrm{Y}}_{2}{\mathrm{C}}_{2}{\mathrm{I}}_{2}$ and ${\mathrm{Y}}_{2}{\mathrm{C}}_{2}{\mathrm{Br}}_{2}$ have been performed to characterize their superconducting state. Our experiments indicate bulk superconductivity with ${T}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}9.97\mathrm{K}$ for ${\mathrm{Y}}_{2}{\mathrm{C}}_{2}{\mathrm{I}}_{2}$ and ${T}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5.04\mathrm{K}$ for ${\mathrm{Y}}_{2}{\mathrm{C}}_{2}{\mathrm{Br}}_{2}$. An analysis of the specific heat anomalies at ${T}_{c}$ in terms of the weak coupling BCS and the two-fluid model, as well as estimates based on McMillan's formula, reveals strong electron-phonon coupling in the present systems, in contrast to the related three-dimensional superconductor ${\mathrm{YC}}_{2}$ with ${T}_{c}\ensuremath{\approx}4.0\mathrm{K}$.