Ok so here's the reality. It doesn't matter how hot she is (and she IS!). It's what she thinks of herself.
Our society places absolutely enormous pressure on women to adhere to a fantasy of the 'ideal woman' in appearance, and anything less means they are ugly. Few women who are 20 can even achieve this fantasy ideal, and virtually none past 40 could so without a few staff members, and a non-stop workout routine. It's just not realistic nor attainable.
Time after time after time again, I see posts on this forum where the wife of the couple feels negative about her appearance, and doesn't want to dabble in the lifestyle because she's certain she's going to be thought of as ugly, and nobody would want her. Ok so problem one; their husbands are the only men in the world idiotic enough to find them attractive? Obviously that's false. Problem two; it doesn't matter what you look like. You could look like Jeri Ryan as Seven of Nine (see Baconhead's avatar above) and some men would go for someone else. All you can do is put your best foot forward, look, act, and feel your best and let potential play partners decide if they want to engage you or not. The ones that don't are saving you time. Third; a woman with the best body and the worst personality is...at least for me...going to find I'm not interested in the slightest. A woman with below average looks but a great, engaging personality is going to find I'm very interested.
So, you can't convince her. Let her read the replies and maybe she'll make up her own mind differently than she does now. Another possibility; go to a swinger meet and greet. You don't have to play, nor is there any pressure to play. Just go and meet people. I think you'll find your wife draws a lot of attention, and she will notice it. It's a safe environment within which to try that. If you want to try something a bit more risque, have her dress up nicely and sit down at a bar in an upscale hotel. You can be there, but not with her at the bar. Go get a booth or table somewhere you can see her, but not right next to her. You're her safety net. Chances are, traveling businessmen will be attracted to her like a set of keys to a supermagnet. She doesn't have to leave with them of course, and the two of you can have a signal that she can make which asks you to join her if a guy is being a problem. Like, setting her purse in a particular way, or turning out from the bar on her stool.