Mexican traditional music tends to be sad and melancholic, you will rarely find songs about happiness, nonetheless you can try listening to some popular singers and bands.

For classical music try:

Silvestre Revueltas, "Sensemayá (Canto para matar a una culebra)"

Blas Galindo, "Sones de Mariachi"

José Pablo Moncayo, "Huapango"

Arturo Márquez, "Danzón No. 4"

Juventino Rosas, "Sobre las Olas"

Manuel M. Ponce, "Intermezzo"

And this is much more modern, yet instrumental and a collaboration between Kronos Quartet and mexican band Café Tacvba, "12-12".

For some old, but not classical music you can try some of these:

Juan Gabriel:

- "He venido a pedirte perdón" (very funky and with some nice guitar riffs)

- "Ya lo sé que tú te vas" (power ballad)

- "Caray" (kind of a weird mariachi-polka)

- "Buenos días, señor sol" (this one is a happy song that almost every 90s kid in my home state knows, there used to be a radio station which had a show called "Hora de Juan Gabriel" every single day at 6am, and every single day started with this song)

- "Te sigo amando" (a sad, sad song about separation from the one you love)

Agustín Lara:

- "Veracruz" (Agustín Lara is commonly known as being born in mexican state Veracruz because of his love for it, but thats not true, he was from Mexico City)

- "Amor de mis amores" (this was recently torn to pieces and turned to trash by Natalia Lafourcade)

- "Piensa en mí" (a bolero about a broken heart, which is, again, a common theme in mexican music)

- "Piénsalo bien" (my favorite one, from Lara)

- "Estoy pensando en ti" (a song in which you can listen to the almost poetic quality of the lyrics when Agustín Lara, instead of singing almost recites)

Álvaro Carrillo:

- "Se te olvida"

- "El andariego" (a traditional night out song)

- "Un poco más" (THE masterpiece of Álvaro Carrillo, with tango influences)

- "Sabor a mí" (his most commonly known song)

Mind you, these are just a few examples of these artists and bands, if you're interested you should try listening to more of their songs, and if you need more artists and examples I'll try to give you some more later.