Selling something on eBay can always be profitable right away provided that what you're selling you're getting at a cheap price. Buying a website that's already profitable and scaling it/collecting the monthly income wouldn't be profitable right away but it would bring in some nice passive income and you would be able to recoup your losses within a few months.
Those aren't the only ways but they're some of the easiest/quickest. The other options would be to build your own website that provides a premium service or products that people need.
It's possible to create a source of income right away though as long as you can find a little bit of start up money to fund your project. Like I said, with eBay or craigslist you could make your business profitable in just a few days or less, that's probably the fastest. It takes smarts, hard work, dedication, (usually) money, and skills (sometimes even a team) to implement successful solutions. I don't know what you're trying to make money from or how you want to make money so I can only give you a general idea of what it takes. A good note would be that it also takes patience.