Create your own diploma. This is an option for children who do not plan to attend college, or children who do not need an official diploma for their chosen college. The homemade diploma gives the student validation that he has completed high school.
Take the GED test after you have completed all of your high school courses at home. If you pass the GED test, you get a diploma.
Sign up for a correspondence school. There are public ones, faith-based ones, ones that have a required curriculum, and ones that allow you to use your own curriculum. These schools can produce official transcripts and diplomas.
Find a private school that is willing to allow you to homeschool. You may have to report grades each semester and have your child tested, but your child will be awarded a diploma from that private school upon completion of the proper requirements.