To start things off, I recommend reading "A Puritan in Babylon" by William Allen White. It has a breezy, approachable style and can easily be digested in a couple of nights. I must raise the caveat that White, although a Republican and friendly to Coolidge, paints a distorted picture of the man and ultimately pins the blame on both Mellon and President Coolidge for the Great Depression. Of course, history shows that is totally wrong.
A book with more substantial meat and free from bias is "Coolidge: An American Enigma" by Robert Sobel. It's a tad bit ponderous in terms of presentation than White's effort but is far more revealing of the truth about this truly great president.
Additional ping to the best and brightest of FReepers when it comes to history: nathanbedford and lentulusgracchus. They may have additional recommendations.