'S far as I know there is no actual song called "New Mexico, Land of Enchantment". Maybe the one you are looking for is this, which was written by the daughter of Pat Garrett (the man who shot Billy the Kid), and was adopted as the state song for, naturally, New Mexico:

O, FAIR NEW MEXICO
Written by: Elizabeth Garrett

1. Under a sky of azure, where balmy breezes blow,
Kissed by the golden sunshine, is Nuevo Mejico.
Land of the Montezuma, with fiery hearts aglow,
State of the deeds historic, is Nuevo Mejico.

CHORUS: O, fair New Mexico, we love, we love you so.
Our hearts with pride o'erflow, no matter where we go.
O, fair New Mexico, we love, we love you so,
The grandest state to know, New Mexico.

2. Rugged and high sierras, with deep canyons below,
Dotted with fertile valleys, is Nuevo Mejico.
Fields full of sweet alfalfa, richest perfumes bestow,
State of apple blossoms, is Nuevo Mejico.

3. Days that are full of heart-dreams, nights when the moon hangs low;
Beaming its benediction o'er Nuevo Mejico.
Land with its bright manana, coming through weal and woe;
State of our esperanza, is Nuevo Mejico.


Regards,
A