First, I think it wonderful that you have chosen to help others in your age range. Personally, I have seen a lot of growth in this segment as clients are now coming to me more often who are in their 50s and 60s. I think it is a smart choice, and although you will most likely train individuals of various ages, having a specialty such as a senior population would be very beneficial. The baby boomers want to take care of themselves, and people are living longer–there is a great need for trainers in this age population. All factors of exercise, balance, and general health and wellness are very important to them.
You can reach out to your local communuty center or Y as a start for seniors. I have my own in-home business, but also work at my local community center–and the senior center is hopping with activities.
Also, put your profile on LinkedIn to reach out to some corporate contacts. Join your local Chamber of Commerce–you will meet a lot of people in your community who can refer clients to you. Also, making connections with physicians, physical therapists, and chiropractors is very helpful. I would even try your local country clubs for the private sector that you are seeking.
Also, if you are looking to teach a class to seniors, you could look into holding classes or even doing presentations for some local churches.
Hope this information helps and best wishes to you.