How can I increase my chances of having my boss approve this schedule change?

I work at a help desk. Right now, I work every day but Tuesday and Wednesday. I'd much rather have Saturday and Sunday off. The real reason for this is that well, I suffer from depression and loneliness and I want to improve my well being by being able to meet up with and hang out with people when they are off work: Saturday and Sunday.

I'm scared that saying my reason for asking for this is for my mental well being will raise a lot of red flags. I'm a Contractor so I kinda feel I walk on thin egg shells. My contract lasts through February so I don't exactly wanna just wait it out. How can I ask for this professionally in a way that gives me the best chances of getting this request. Willing to work any time.