Our current itinerary has a 6 hour stop ove in Madrid before we fly to Rome. Are there any alternatives? We are on American airlines but are open to other airlines.
Thank you.

You are kidding, right? How is anyone supposed to answer a general question that depends on specific time information?

One alternative: a direct flight from your home airport to Rome.

I was trying to find out if there are small airlines that within Europe and have flights from Madrid to Rome. We have Southwest in the U.S.

look at www.whichbudget.com
What day of the week---what time of day??

Is your current flight booked al the way through (home to Madrid to Rome) on American and/or American partner airlines? A booking on one airline will protect you in case something goes wrong with the home-Madrid flight.

Looks like budget airlines that fl that route include Ryanair, Easyjet, Vueling, and Air Europa. They may not offer fights every day.

http://www.skyscanner.net/