Ryanair ran a service on this route 2 years ago for 6 months, However, because they advertised it badly, they only got 50% loadings.
They decided not to persevere with the service, which I think was wrong.
There are not low-cost flights between Madrid and Faro.
Your options are:
Low-Cost Flight - Madrid-Lisbon and then Bus/Train Lisbon - Faro
Bus/Train - Madrid to Seville
Bus - Seville to Faro
Have a look at these posts on my blog which may help.
http://barlaventostravelblog.blogspot.com/search?q=Madrid+Faro
