Here's what worked for me, and maybe it'll work for you.Be patient and honest. Have several discussions with her, finding out her issues and roadblocks. Talk about her fears. Keep it open and honest, but use this time to find out her doubts. Don't try to solve them at first, just listen. Once my wife and I really started talking about it, she got past the typical anti arguments (mostly false and Hollywood driven), and I started to find out her real issues. Over time, start addressing these fears with sound answers and facts, try to keep your emotions in check.
While listening to these talks, start formulating your true reason for carrying. My reasons were primarily for security and "self-preservation" of the family. If you have kids, be sure you have a plan to address the security of the gun (home safe, car safe, etc). Talk about how you plan to educate your kids on gun safety.
It took me about a year to convince my wife it was a good idea, and she is ok with it now. But once she understood why I wanted to carry, and how I was planning on doing it, and how I would protect/educate the kids, she came around to it.
One discussion point I used that was very effective was:
When we're 90 years old, I really hope you'll hit me in the back of the head and say "See I told you so, you didn't need to carry that piece of metal around for all of those years, see you didn't need it." I'd rather have that conversion with you than the "I wish I had been carrying when XYZ happened many years ago, I could have prevent ABC from getting hurt."
I asked her which conversation she'd rather have when we're 90.
Furthermore, get some training, even if it is basic. Learn to use the gun correctly and safely. Show your wife that you're serious about safety. Start competing in IPSC and/or IDPA. This will get you familiar with your gun.
Good luck, but be patient, and she'll come around.
Just my $0.02.... Ryan