I think I'm tired of my best friend's relationship
How can you think that about them? Why do you dislike your best friend's relationship?
Well, I think it's really childish and need some serious intervention.
As long as your best friend is not being hurt, you should attempt to ruin her relationship. What goes on in her relationship does not concern you and you should respect her happiness. Instead of focusing on her relationship, you should find someone that you can connect with.
She is not in love with her boyfriend but she still have sex with him.
Has he told you she feels that way, if not then I believe it's best to not interfere with them. It's their life and relationship, and you should just let them figure things out instead of breaking them up. How about just supporting your friend whenever she needs advice?