Many practical wireless communications systems select their transmit rate from a finite set of modulation and coding schemes, which correspond to a set of discrete rates. In this paper, we therefore formulate a joint coordinated precoding and discrete rate selection problem for multiple-input multiple-output (MIMO) multicell networks. Compared to the common assumption of using the continuous Shannon rates as the user utilities, explicitly accounting for the discrete rates more accurately models practical wireless communication systems. The optimization problem that we formulate is combinatorial and non-convex, however, and is thus hard to solve. We therefore rewrite the problem using a discontinuous rate function, which we then bound using its concave envelope in some domain. Based on block coordinate descent, we provide a convergent resource allocation algorithm which can be implemented in a semi-distributed fashion. Numerical performance evaluation shows performance gains when the discrete rates are optimized using our model, as compared to the traditional methods which use the continuous Shannon rates as the user utilities.