In high school and college I built furniture for a job. The money is in the custom work. I built a custom desk in the mission style for the superintendent of the school. I built new kitchen cabinet doors for another client. Another big project was a corner shelf entertainment cabinet. A few smaller projects like shelves, picture frames, etc. were completed along the way. Over three years I probably netted about $8,000 working part time in the summers (i.e. full time hours for a few weeks at a time). I targeted a rate of $25/hr in the early 2000s. This was in a small town in the Midwest, so HCOL could easily double that if you have the skills/portfolio to convince customers that you are good.
I would recommend looking into what requirements your area has for handymen/contractors. In my city, if you do work on another persons home that requires a permit, you need to be licensed contractor. Licensing here requires taking an exam, getting insured and bonded. Those are some pretty big overhead costs for a side business. Personally, I'd stick to small jobs that don't require permits in your area and get an umbrella liability policy. Otherwise, the furniture/small craft woodworking projects are good way to go as there is no licensing/permitting for building a bookshelf.