Serendipity: an aptitude for making desirable discoveries by accident.*
Serenity: the state or quality of being serene, calm, or tranquil.
Both of these words lead the imagination to a state of happiness. If one were to be the recipient of the actions these words define, it would only work to make the person have a better life.
Some say that being a pessimist means you'll never be disappointed and sometimes you'll be surprised things didn't turn out terribly. While there may be some truth to that, there would still be no happiness because one would never expect happiness and so never see the happiness, it becomes pushed aside. The pessimistic surprise is not serendipity. Serendipity lends itself more to the optimistic side of things. Optimists can find joy in places that pessimists cannot.
Serendipity is discovering a five dollar bill in your winter coat pocket when the cold season comes. It is finding an extra french fry or two in your bag that fell out of the container. It's running into an old friend at the store that you've been thinking about recently. Serendipity is walking outside after a storm and finding a double rainbow crossing the sky.
If you notice in the definition of serendipity, it says an 'aptitude'. An aptitude is an ability. Optimists have an aptitude for making desirable discoveries by accident, for serendipitous moments, because they can see the good in a situation. They take notice of the joy in the world around them. It's a happy person that has the gift of serendipity.
Serenity is a state of peace and calm. The feeling you get lying the in warm grass watching fluffy white clouds float by. The feeling you get looking out over the valley from a mountain top. The overwhelming emotion of being unconditionally loved and accepted. Serenity is being calm, peaceful and tranquil without terror, anger, sadness, or turmoil. It can be hard to have serenity in this chaotic world, and it may only come in patches, but those patches of serenity get us through the hard times.
Malcolm Reynolds, in the show Firefly, names his ship Serenity. I think it's probably because flying his own ship that can take him anywhere in the immensity of space is probably a feeling of freedom and serenity. There's a sense of serenity in being able to be free to do what you like, when you like, where you like.
If one tends towards optimism, there can often be serendipitous moments and feelings of serenity.
*Definitions provided by dictionary.com