The typical at home client is the 30-40 something housewife. Determine the area you want to train in (I would recommend high end neighborhoods) find the free local publications that appeal to their interest ie;Child magazines, retail magazines etc. Advertise in these publications your cost is minimal but the readership is huge. Also once you find one at home client you must work at developing a relationship that makes them want to refer you to their friends, there is a great possibility that their friend will share similar interest and be in a similar economic situation.
Marketing is tricky no matter how you go about it. Let the word out that you offer such a service and get the word of mouth started. Help a few people start at home programs that they can keep up with on their own and have them give testimonials on your profile, blog, or website. Train a few people at their house for free and get some recognition as a go to trainer for this sort of thing.
I offer free community lectures. I work with older adults and part of that lecture involves an “assessment” – ie sit to stand without using arms. Those that are unable to perform, I explain the safety hazards and fall risk of not being able to complete. I have other examples as well. I can usually get a client or 2 each lecture.