You have perfect pitch yet can’t harmonize?
Hmmmmm, usually the chorus is a good place for harmonies. Try figuring out the vocal line on the guitar and then experiment with different 2 note chords till you find something you like. Then just sing it with the guitar until you can do it.
It can take a little practice to not sing the same notes as the lead.
Or maybe try and lean a few Bad Religion songs. I really like the harmonies they use. They do it in just about every song… In fact I can’t think of one that doesn’t…