This week's book giveaway is in the OO, Patterns, UML and Refactoring forum. We're giving away four copies of Refactoring for Software Design Smells: Managing Technical Debt and have Girish Suryanarayana, Ganesh Samarthyam & Tushar Sharma on-line! See this thread for details.
If you look at the value for AlarmManager.INTERVAL_DAY (or any of the other constants) you will notice that they are millisecond values. So just determine the number of milliseconds between now and the desired wakeup time and pass that value to AlarmManager.set().