Solved.
What is the name of this Mexican tune, that is being played on this Barney episode?
Please listen at: 10:28 - 11:28:
http://www.youtube.com/watch?v=4B_y-Rx0NuQ
I remember hearing it at a Mexican restaurant.
Dancing Rebecca can also jam to this Midnight In Moscow tune by Kenny Ball:
http://www.youtube.com/watch?v=o0xeETLadI4
Anyways, What is the name of that Mexican tune, as mentioned?