While not requiring bravery per se, the act of suicide does require a great deal of personal courage and conviction. Most suicide attempt fail because the means were more important to the person than the end. The act is usually more of a cry for attention than anyting else.
That being said, I can't imagine Ennis succesfully comitting suicide. He possesed a great sense of right and wrong (albeit quite skewed), and his love for his children, and even Alma would prevent him from doing that. Ennis was never one to crave attention, and I dare say would go to any lengths to avoid it. He was the type to think to himself "what would they be saying about me afterwards".