Well, your residency should give you an AAP membership as a resident which will provide you yearly PREP question books. Additionally, people usually go with "Laughing Your Way" or "First Aid" to help supplement the PREP questions with text. I assume that is what you are referring to for the final board exam.
As for residency itself, I'm not sure a book will help you. Most residents are supplied with Harriet Lane, which I found the formulary to be extremely helpful, but that was in the days before computer orders and entry, so I'm not so sure it is as much value as it used to be. You should read up on the patients and diseases you encounter either via review articles or UpToDate (which people give flak to, but are fine review summaries and peer reviewed). For more broad, continuous reading, Peds in Review, which comes with the AAP membership as well, gives good summaries on various topics and is almost always board related. You can buy an actual textbook, but I think it of limited value for actual residency (with the exception of reading up on patients, but textbooks aren't very cost effective). I think I bought Nelson's and opened it maybe 3 times.