I’m looking for books that had to do with what I would describe as monkeys that do coupling all the time. I cannot remember the name of book or author, but I really enjoyed it and would like the names so I can look for them.
Your description is sadly not much to go by, but if "coupling" means something different than copulation, there is a story where "monkeys that do coupling" is a constitutive story device: Robert_Silverberg's novel At Winter's End (1988); it did appear as an SFBC publication.
The main characters in the novel look like monkeys, but have human intelligence, while humans as a species have died out over the eponymous winter, an ice age which ends as the story begins. One special ability of these monkey-like sophonts is a mind-to-mind coupling they call "twinnering" (or something similar; I'm retranslating from German here). Not unreasonably, twinnering is considered significantly more sacred and intimate than copulation.
Publication dates haven't always been a great guide for story-identification questions, so let me go a bit outside the window of opportunity and suggest Will Self's novel Great Apes (1997).
After a night of drug use, Simon Dykes wakes up in a world where chimpanzees have evolved to be the dominant species with self-awareness, while humans are the equivalent of chimps in our world.
My predominate memory of this book is the obsession with sex by the Chimpanzees and the central place mating holds in Chimp society. Simon has significant trouble integrating into his new life, as per the goodreads description.
He can't bring himself to use gestures rather than speech to communicate. He also finds it difficult to mate publicly or accept social grooming.
If I recall correctly Simon's girlfriend in the human world was a childhood rape victim, having been abused by her father. The same individual is in therapy in the chimpanzee world because her father wouldn't have sex with her.