Sometimes you can't avoid negative people in life. Here's a how-to cope with them.
Don't be around that person all the time if you can help it. If you live with them, try to spend as much time as possible with other family members or with friends outside the home. Do something that doesn't involve the other person too much. You don't want to learn their ways of thinking and add it into your own mind.# When you do spend time with them, try to have a positive attitude yourself. Balance it out! Try to think of good qualities about that person. Pay good attention. Everyone likes a bit of attention whether they think they do or not!
Be very nice to them. If they are having a problem that you know you may be able to solve, jump in, and give them a hand. Do something unexpectedly sweet, like chores for a day, invite them to watch a movie with you, take a walk together with them, or stop doing something you know annoys them.
Tell them how it is making you feel when they are negative around you. Be constructive; tell them something else they can do and or how they can change. Encourage, don't force. Most people don't like lectures on how to behave, especially when it's pointed towards them that they are horrible or so.
Make a "hot-word" like "oranges", "butterflies", "ocean soul", etc. That you agree with the person you are going to say each time you hear them say something negative - this will act as a good reminder for them and will draw their attention to their own negative comments. Some people do it by habit. In a bad way.

Try to understand why they act the way they do. There may be many hidden issues that you don't know about.
Try to get close to these people; open your heart.
Inspire them to change. Let them see the bright side and how it is to be an optimistic person.
Include them in your life; make them feel needed. Most people are negative because of low self esteem, and by making them feel needed, you make them feel unique. Be a unique individual yourself and help let them breathe easier!

Warnings:
Don't let negativity from these people turn you into a pessimist! Nothing ruins the happiness in one's life more than anxiety and letting their depressing imagination take over. Be yourself; love optimism!
Someone who is negative all the time may be depressed. Ensure that they are not planning to harm themselves or others. Someone who is suicidal should be encouraged to seek professional help.
Be aware of your presence and how the other person feels when you are around them. Perhaps they may be envious of you and what you have. Prove to them that you are not a threat, and that you could be a loyal friend they can come to when life gets hard.