There are plenty of ways to teach public speaking in your homeschool!
You can focus on speech and debate. It's pretty intense, and takes a lot of work on the part of the child. On the other hand, if your child likes it, it's a great way to include English and Social Studies through that delight directed learning. Try contacting these organizations.
You can focus on public speaking. This may be less intense, and usually involves giving a simple speech each week, or month, or whenever it is convenient to attend the program. Many church programs include public speaking. Try contacting these organizations.
You can focus on practicing public speaking in the context of other classes. Using a DVD series or homeschool class, your child learns basic public speaking. Then they practice their skills when presenting oral reports to family or friends. We used to give monthly oral book reports in our homeschool group, and it was great fun! All grades participated, and we celebrated with pizza as a group. [Note: This post contains affiliate links. If you click and buy I may make a few pennies, but not enough for a latte.]