1960’s/70s cheap science fiction. It involved a colony that had female creatures who had evolved pink skin, and tails. Several of these creatures were featured in what appeared to be a painting on the cover of the mass market paperback I had. The main male character was sent by his company to check up on/audit the colony in some way. The female creatures were a second class of citizens who had small tattoos who indicated the type of work they did at the colony. The main male character falls in love with one of the female creatures and they attempt to escape the colony. Their attempt to escape involved a machine called a “spindizzy”.
Probably “The Lani People” by Jesse Franklin Bone.
I googled spindizzy, as I’d only come across it in the ‘Cities in Flight’ series by James Blish. Apparently an author called Jesse Franklin Bone also used it. You might look into his books ‘The Lani People’ and ‘Confederate Matador’
You are definitely describing “The Lani People” by Jesse Franklin Bone, first published in 1962. It’s about a veterinarian named Jac Kennon who is hired by a large corporation to examine the “animals” (the women with tails, the eponymous Lani) on another planet. The tattoos indicated their sub-breed pedigree. Spindizzy was the method of interstellar travel throughout the book.