You don't want too thick of a coat since that will make the fabric feel too thick and starchy (It's going to feel a bit stiff anyway). A roller will put a nice coating on the fabric without getting a heavy layer on. I use small rollers since they will get into the folds and nooks of the fabric more easily.
But I'm getting a bit ahead of myself - first things first. Test the fabric on a patch that won't show. Some material isn't suitable for painting -- some couches are just foam with a thin cover. One friend painted a foam couch and it soaked up a gallon of paint before she figured out that it was never going to dry. I used less than half a gallon of latex wall paint on this couch.