  Coupled discrete models abound in several areas of physics. Here we provide
an extensive set of exact quasiperiodic solutions of a number of coupled
discrete models in terms of Lam\'e polynomials of arbitrary order. The models
discussed are (i) coupled Salerno model, (ii) coupled Ablowitz-Ladik model,
(iii) coupled $\phi^4$ model, and (iv) coupled $\phi^6$ model. In all these
cases we show that the coefficients of the Lam\'e polynomials are such that the
Lam\'e polynomials can be reexpressed in terms of Chebyshev polynomials of the
relevant Jacobi elliptic function.
