Piquito de oro literally translates to "little beak of gold." It's a charming and unique term of endearment that isn't commonly found in everyday Spanish.
In this song, Ramón Ayala uses it to affectionately refer to his beloved. It implies that her kisses are precious and highly valued, like gold, making it a very sweet and memorable phrase to describe a loved one.
Ramón Ayala spends this norteño waltz describing one person and one feeling, and he never leaves either. The opening line sets the whole stake at once — "Yo tengo un amorcito que la quiero más que a mi vida" (I have a sweetheart that I love more than my life) — and everything after it is detail on that claim. He says he'd die for her and that she knows it, and then he narrows the song down to a nickname: he calls her, tenderly, his piquito de oro, his little golden beak. It's the kind of pet name that only makes sense between two people, which is exactly why he keeps repeating it.
The second half of each verse is about what she likes, not what he wants: "Le gusta que la bese y que le diga mi lindo tesoro" (She likes that I kiss her and that I call her my lovely treasure). Then the chorus turns into an announcement — Ahí viene (There she comes), four times over, as the accordion swings underneath. He isn't pleading or courting; he's watching her walk toward him and naming her out loud. The song's whole shape is a man saying the same happy thing until the band stops.