YES! There are several government teaching programs available in Spain other than the Cultural Ambassadors Program.
These programs come with a student visa and each has different costs and requirements associated with them, so be sure to do your research to ensure you qualify. They include:
Meddeas - Language Assistant
BEDA Program - Language Assistant
UCETAM - Language Assistant
UP International Education - Language Assistant
Conversa Spain - Language Assistant
Fulbright Spain - Teaching Assistant
Read More: Spain Government Programs Quick Guide