Anybody can take AP TESTS, even if you don't take AP CLASSES.
An AP test can be marvelous outside documentation for learning, and it can be a real boost to your college application if you are gearing up for a very selective school, or need big scholarships. But you don't need an AP course in order to take an AP test. Read more on the College Board website. "You can take as many AP Tests as you want; in fact, the AP Program doesn’t require you to take an AP course before taking an AP Exam." Registering for AP Exams
AP exams are not like other tests. The last many hours, and are really long essay tests. For each test, purchase an AP Study Guide in that subject. Using the study guide, give a timed, full practice test at home. Then see what the score will be. If you get at LEAST a score of 4 at home, or hopefully a score of 5 at home, then you'll know your child should do well enough on the test.
You can take all the APs you want to each year, but be careful of your expectations. It's difficult to take more than 2 AP exams each year because they require so much study time. However many you take, make sure they will pass the test at home before taking it for real.
If you want to teach an AP class at home, you need approval from the College Board. However, you do not need to write and get AP course approval if you want to. If you get course approval, put"AP" by the name of the class on your transcript. If you do not get course approval, put "Honors" by the name of the class, and put the AP test scores on the bottom of the transcript.
Generally speaking, colleges grant college credits based on AP exam scores, not on AP courses. Each college is unique, so do your research on your college policy. Have you looked at the AP policy for the college you might apply for? What does that college policy say?