We all have different personalities, and some people do seem to have a natural bent toward unhappiness (just as some have a natural bent toward happiness and optimism). Sometimes the reasons are obvious (an unhappy childhood, for example) but often they aren't.
I'm thankful, however, that you've made an effort to be this woman's friend, because I suspect she may not have many friends. (After all, who wants to be around a gloomy, negative person all the time?) As part of this, ask God to help you be a patient and good listener -- and also a wise advisor and encourager. You may find, for example, that she has a very negative view of herself and feels she's worthless, and you can help her realize it isn't true. The Bible says, "A word fitly spoken is like apples of gold in settings of silver" (Proverbs 25:11, NKJV).
The most important thing you can do, however, is to help her see herself the way God sees her. God loves her just as she is; He loves her so much that His Son gave His life so she could become part of His family forever. The Bible says, "This is how God showed his love among us: He sent his one and only Son into the world" (1 John 4:9).
Then pray for her, not only that she'll become a more cheerful person, but also that she'll turn her life over to Christ. And if you've never made Him the center of your life, do so today.