[The series and its rules are explained here, where you will also find links to the songs for the other states.]
31:1. El Paso: 'Out to the badlands of New Mexico'. (1, 2.)
31:2. Mercenary Song: 'Met Hank out in New Mexico'. (1, 2.)
31:3. Route 66: 'You'll see Amarillo and Gallup, New Mexico'. (1, 2.)
31:4. Two for the Road: 'You had Georgia's New Mexico'. (1.)
31:5. New Mexico: 'To the god-forsaken country / They call New Mexico'. (1.)
31:6. White Freightliner Blues: 'Ah, New Mexico ain't bad, Lord / And the people there they treat you kind'. (1, 2, 3.)
31:7. Let Me Die In My Footsteps: 'Nevada, New Mexico, Arizona, Idaho / Let every state in this union seep deep down in your soul'. (1, 2, 3.)
31:8. Goin' Back To Texas: 'I've gone through Arizona, right through New Mexico'. (1.)
31:9. New Mexico Rain. (1, 2.)
31:10. If I Were The Man You Wanted: 'Then don't linger in New Mexico'. (1.)
31:11. Santa Fe Cantina: 'It's a long way back to New Mexico'. (1, 2.)