It sounds like you want a notification to be posted to the notification bar.
If so I advise using an alarm.
However, chances are if this is days in the future, the phone may be shut off. So you should store when the alarm should go off, create a Broadcast receiver for the on boot complete event (this requires a permission), and re-setup the alarm when the boot is complete.
This should allow the notification to appear, independent of the apps life-cycle, as long as the app is not uninstalled.
Note: You will have to calculate the milliseconds between the date for the alarm, and the current time. Calendar should help.