Your most effective entry point to the subject is through the person's doctor. When the suggestion to use incontinence products comes from him or her, you avoid getting into a incontinence in older women and incontinence in older men, there are many medical causes that can be treated and cured.
battle of wills or an argument -- or being seen as the "bad guy." Besides, it's smart to link the discussion to a doctor's visit, because for both
You want to be empathetic but not shy when discussing incontinence products -- even if you find the topic embarrassing or are worried about invading the other person's privacy or dignity. Jump in: "I know this is hard to talk about, Mom, but I have these new panties the doctor told us about. They're made of absorbent material, so if you do have another accident, it won't be a problem. Nobody will know, and later you can change it." If you're embarrassed, admit it (but do so with sensitivity): "I feel weird talking about this, too, but apparently it's a pretty common situation."
Be matter of fact about the advantages: It will save you from being embarrassed if there's an accident, nobody will know, it will save your clothes, it's better for your skin.
If the person still refuses to try, just leave some in his or her underwear drawer and drop the matter for a while. People are often torn between wanting a solution to their problem and getting over their own pride or misconceptions about absorbent undergarments. Be reassuring: "At first it might not seem comfortable or right, but you'll get used to it."
A word about what style to try: New users are often receptive to those that most resemble their regular underwear. Obviously, incontinence products aren't made of silk or lace, but they do come in pull-on male and female styles that will seem more familiar than side-fastening or belted diapers.
A word about language: Most people are turned off by the word diaper. It sounds babyish, which makes it hard for anyone to imagine using them. It can even make the person panic. So try to avoid diaper or adult diaper. Call them disposable panties or disposable underpants or just pull-ups, which is what many type resemble. The person can step into the disposable underwear just as if it were regular underwear, which will make most people more accepting of trying them.