American Libraries recently posted an article about programming for homeschooled kids and their families. There are a lot of great ideas there that you should take a look at, but very few of the ideas are focused on teens. Like any library media specialist knows, teens need to have their reading, research, and library skills in check before college, and those being homeschooled are no different.
In addition to inviting those teens to your regular programming and events, consider doing things for them during the lull of the day, when everyone else is in school. Not all parents who homeschool are necessarily schooled in how to use library databases, scholarly journals, and online media for research projects, so perhaps a small group might appreciate a workshop similar to the ones high school students get from their librarians. You could even designate a special hour a week for drop-in lessons.
On a similar note, homeschools don't employ full-time college counselors, but you probably have a circulating and non-circulating collection of test prep books, college guides, and more. Another unique daytime program you can offer, then, is a college workshop. Invite some current college students, whose schedules also allow them to have some free hours during the day, to answer questions about local schools and essay topics, and see if any of your regular homework tutors can volunteer to come in and help with the process.
Many homeschooled kids participate in things like Cub Scouts, community theatre, and sports so that they're not cut off from the greater community. But what about that good ol' teen stuff that your parents aren't supposed to facilitate for you? You know...angst, sex, peer pressure, body changes. Consider hosting a daytime talk group, possibly broken into male- and female-only groups, where peer mentoring and bonding can happen outside of the home and away from the parents. This is also a great way to look into partnering with community organizations dedicated to youth development or prevention, or to bring in a volunteer or intern, such as a graduate student in counseling. To broaden horizons even more, make it a drop-in after-school talk, where teens from any school situation can hang out. Write a theme on a whiteboard outside the door, alongside some guidelines for safe spaces, and let them guide the conversation the way they would at lunchtime on the bleachers.
Many homeschooling parents form support or social groups. Look online for groups in your area, and then reach out to them to let them know about the resources you already have. Since they're apt to take their kids on field trips, remind them about the museum passes you offer. Put them on a mailing list and let them know about new materials in the library relevant to curriculum and enrichment. Send them a schedule of all the events for teens, but highlight those that are designed specifically for homeschoolers. Or reach out and ask the parents and the teens what they'd like to see in their library.
Host an alternative futures event! If local high schools are only doing traditional college fairs, work with representatives from the Peace Corps, Americorps, and other post-graduation, gap year programs. While any teen would enjoy programming such as this, it's especially relevant to more and more homeschooled teens, who often decide against college or the military post "graduation" in favor of more self-paced, experiential learning like they're used to. This would be a great way to spark conversation between your homeschooled patrons and their traditional school counterparts--what do they think are the best plans for an 18-year-old? What could they never see themselves doing?
Do you have a strong contingent of homeschooled teens in your community? Do you even know?