I'm trying to figure out a backing vocal harmony, but I can't come up with anything I like for the life of me. I feel guilty for asking you guys because I usually never do stuff like this. I mean, I like to figure things as personal as songwriting on my own.

But, I need your help.

The chorus melody is very simple, in the likes of the Beatles or Madonna. So, what I'm asking is....how do you do vocal harmonies in a song? What are some of your own techniques?
Work out the 1st note and sing it and the rest of the melody a 5th higher.

Or, just play it back on loop and experiement.
if you play guitar or piano or something, try hearing the melody and then find something that works with it! it usually works...