What is your background? Have you worked in fitness or wellness or health care? Are you an ‘avid’ exerciser?
If your wife already has a clientele it could be a really great opportunity for you, as one of the biggest issues in starting in fitness is developing a client base. I think you might still will want to do a cost/benefit analysis to look at the cost of the certification /training /insurance etc, as opposed to what you expect to earn, how long it will take to pay back the cost of training etc.
Most people who want to work in fitness do well to get a base, nationally recognized certification, and/or a degree in some related field. However if you are definitely only going to work with this population group, the organization Karin mentions is a really good option that is specific to your needs.
Do recognize though, that how much background you already have will effect how much study you will need to do to be ready to work with clients, especially in this population group which have a significant need for modification, and which varies so much (hence my first question). If you do not have a ton of experience you might want to do a general certification, as well as the specialty one for older people.
Here is a site to compare certifications: