My friend Marty suggests the Lindvall book as well as
H. Thorisson, Coupling, Stationarity, and Regeneration. Springer, New York, 2000.
and points out that coupling is used now in basic textbooks in stochastic processes to prove the ergodic theorem for Markov Chains. So he recommends
Geoffrey Grimmett and David Stirzaker, Probability and Random Processes, 3rd edition, Oxford University Press, 2001.
A monograph that presents the 1975 Stein-Chen method:
A. D. Barbour, Lars Holst, and Svante Janson, Poisson Approximation
A rare accessible discussion is in chapter 2 of:
Ross, Sheldon and Peköz, Erol (2007). A second course in probability. www.ProbabilityBookstore.com. ISBN 978-0979570407.
Link to page for Peköz, which gives further link for book purchase to Amazon:
A number of useful links at