We use variable-pressure neutron and X-ray diffraction measurements to determine the uniaxial and bulk compressibilities of nickel(II) cyanide, Ni(CN)$_2$. Whereas other layered molecular framework materials are known to exhibit negative area compressibility, we find that Ni(CN)$_2$ does not. We attribute this difference to the existence of low-energy in-plane tilt modes that provide a pressure-activated mechanism for layer contraction. The experimental bulk modulus we measure is about four times lower than that reported elsewhere on the basis of density functional theory methods [{it Phys. Rev. B} {bf 83}, 024301 (2011)].