Anime fan fiction--stories written by fans featuring popular characters--has gained a wide following, and a website archiving or promoting fan fiction can gain a lot of ad revenue. Publishing a domain name is inexpensive and ads can be set up through a free resource such as Google. A teen can serve as moderator and gather volunteers to help maintain the site.
A web comic with a teen's own anime art can gain many followers. The creator would charge a minimal fee and set up the comic as an RSS feed for subscribers. Including ads on the web page can also generate ad revenue.
Online art gatherings such as deviantART feature large communities of anime fans. Teens can create a free account and post their art to share with those interested in anime art. Many artists sell prints or copies of their work to make a small income.