Hi there benitacanova! B)
Ah, the common problem of zones and DVD's. Well, I am not familiar with a list of DVD rental establishments in Madrid that rent zone 1 DVD's. That's a bit of a hit or miss search on your part, but it's certainly worth a shot. Please let us know if you have any luck with this.
Alternatives? A couple you may want to consider as far as I can see. The first and simplest is to buy a multizone DVD player at your local Hipercor, Carrefour, Alcampo, Mediamark, etc. They've gone down in price dramatically over the past couple of years and I've seen some multizones for 60-70 Euros.
The second, if you find yourself in a bit more of a technologically inspired frame of mind would be to look into trying to change your DVD player to multizone yourself. This isn't possible with some, so you have to look into it yourself. I found a neat tutorial on the subject
RIGHT HERE!! First, I recommend you read pages 1 through 5 of the tutorial, then look for your make and model using the menu on the left to see if you can '
Free your DVD!'

B)
Another good site that deals with this and many other similar subjects is:
VideoHelp.com.
Best of luck... Please let us know how it goes.....