The orientational diffusion of a nitrogen molecule N-2 in a three-dimensional crystal of argon atoms is studied by using the reaction coordinate formalism and the Bennett-Chandler approach. To study the two-dimensional orientational diffusion the reaction coordinate formalism has to be generalized to multichannel reactions. The rate coefficient for the motion between the six stable orientational states is determined from correlation function expressions, which include corrections to transition-state theory due to recrossings of free energy barriers. At high temperatures the simulation results are compared with results obtained by standard molecular dynamics methods. At low temperatures the transmission coefficient is computed and the dependence of the plateau value upon the density of the surrounding argon matrix and upon the isotopes, chosen to form the N-2 molecule, is investigated.