I'm thankful you want to help your sister; I'm afraid some people don't want to get involved with someone who's hurting. Perhaps we don't know what to say, or we're afraid we'll only make things worse. But whatever our excuse, the Bible tells us to "Carry each other's burdens" (Galatians 6:2).
What can you do? First, try to understand what your sister is going through. No, her marriage hasn't been very happy, but now she's facing the humility and pain of rejection -- which can be even more devastating. She also may be burdened with guilt, blaming herself for what went wrong (even if she shouldn't). In addition, she probably fears the loneliness, uncertainty and financial burdens that come from suddenly being alone.
Then learn to be a good listener. It's tempting to come up with cliches or quick "solutions" to make someone feel better, but (as you've discovered) this seldom works. The Bible says, "Everyone should be quick to listen, slow to speak and slow to become angry" (James 1:19).
Most of all, pray for her, and encourage her to turn to God and find her strength in Him. God knows what she's going through, and He loves her and wants to help. And He will, as she opens her heart to Jesus Christ and trusts the future into His care. In addition, many churches today sponsor divorce recovery workshops, and you might help her find one in your area.