Writing-Game-Center-Apps-in-iOS is a project mainly written in Objective-C, it's free.
O'Reilly's Writing Game Center Apps in iOS Book's example codes
This repository contains all example codes from the O'Reilly book "iOS 4 Programming Cookbook" by Vandad Nahavandipoor
You can find the book on O'Reilly: http://oreilly.com/catalog/0636920020349/
Or on Amazon: http://www.amazon.com/Writing-Game-Center-Apps-iOS/dp/1449305652/ref=sr_1_1?s=books&ie=UTF8&qid=1308385773&sr=1-1
Or other major book sellers