For some reason, this has not been defined on urban dictionary until now.
Anyways, if you are looking for the definition. It's self explanatory (The opposite of happy birthday, used as an insult when it is someone's birthday).
Jacob : Today is my birthday! Will you come to my party?
Micah : Absolutely not, and unhappy birthday!
When David went to prison all the anal rapists laughed at the tramp stamp which read "oops" that they could read through his especially hairy unhappy trail.
Is a trash bag that is full of normal trash and puke but doesn't throw it away and then someone goes to throw something in the bag that might cause the entire bag to tip over causing a disgustingmess.
When you puke in a trash bag and someone goes to throw something away on top of it and you go to stop them by saying, "No, don't do that. That's unhappy trash."