The two verses given by Escamillo seem to be the original Spanish lyrics (or as close as one can get in a song that is folk or has become folk.
Mexican sources allege that it came to the Americas in the 16th century.
As Joe suggests, it is not a rima infantile (children's rhyme), but a celebration of one's homeland.
I am searching through F. R. Marin, 1882-1883, "Cantos populares Españoles," a massive book of some 900 pages. As would be expected, it is not included in 'Rimas infantiles,' but I haven't figured out whether it is in 'Amorosos,' which he very broadly defined, or another section, or is not included at all. The book has no song title index, so looking up verses is not easy.

A third verse appears in some Spanish and Latin American versions on the web. It is without apparent religious significance. Joe posted a similar verse, but with a religious add-on.
All religious lyrics seem to be revisions, but without seeing old versions, this is just an opinion.

3
De colores, de colores brillantes y finos se viste la aurora
De colores, de colores son los mil reflejos que el sol atesora
De colores, de colores se viste el diamante que vemos lucir
y por eso los grandes amores de muchos colores me gustan a mí
y por eso los grandes amores de muchos colores me gustan a mí.

kiri=quiri, both spellings occur in Spanish.