We study the numerical approximation of doubly reflected backward stochastic differential
equations with intermittent upper barrier (RIBSDEs). These denote reflected BSDEs in which
the upper barrier is only active on certain random time intervals. From the point of view
of financial interpretation, RIBSDEs arise as pricing equations of game options with
constrained callability. In a Markovian set-up we prove a convergence rate for a
time-discretization scheme by simulation to an RIBSDE. We also characterize the solution
of an RIBSDE as the largest viscosity subsolution of a related system of variational
inequalities, and we establish the convergence of a deterministic numerical scheme for
that problem. Due to the potentially very high dimension of the system of variational
inequalities, this approach is not always practical. We thus subsequently prove a
convergence rate for a time-discretisation scheme by simulation to an RIBSDE.