Sonriendo means "smiling" and is the present participle of the verb sonreír (to smile). While sonreír is a common verb, its use as a participle in this context is particularly engaging.
In "Buenos Días Señor Sol," Juan Gabriel sings, "Y sonriendo haré las cosas con amor" (And smiling I will do things with love). This emphasizes a conscious choice to approach life with positivity and affection, making it a powerful and uplifting word that sets the tone for the entire song.
Juan Gabriel opens the song the way he opens the day: he wakes up, sees the sun in his window, and decides to try again. "Todas las mañanas que entra por mi ventana el señor sol" (every morning Mr. Sun comes in through my window) sets the scene, then he gives thanks for it plainly — "doy gracias a dios por otro día más" (I give thanks to God for one more day).
From there the song turns into a string of small greetings, said out loud to whatever the day brings: "Buenos días a la alegría... buenos días a la vida... buenos días señor sol" (good morning to happiness... good morning to life... good morning, Mr. Sun). It reads less like a love song than a daily habit — smiling on purpose, "sonriendo haré las cosas con amor" (smiling, I will do things with love), and choosing, one morning at a time, to keep trying to be better.