I don't buy presents for my coworkers and friends. Instead I write poetry to them.
I started combining their names with whatever words rhyme with it, sometimes with very funny results. However, Id like what I write to sound more elegant and intimate.
I also tried combining their physical features with whatever rhymes with nose, arm, eye... Sometimes results are also funny.
If it helps, most of my coworkers are women, all of them are strictly platonic friends. Id also write a poem to a male coworker.
I'd really hate it if someone wrote a poem to me. Even worse if it was a gift.
I'd actually prefere no gift at all, than a (funny) poem or a song to be honest.
Just off the top of my head but I think you’re on the right path when it comes to sounding more eloquent. Poetry probably came from people messing around and playing with words to find what sounds interesting.
You’re already good to go on rhyming. So maybe just try for different rhyme schemes.
You might could also add other whatever-they’re -calleds like alliteration, consonance, metaphors, etc. Each of those are just a tools in the poet’s toolbox.