Not sure how you reacted to your wife's statement, but the right answer right now is, "I can't blame you for feeling that way. And I know it's not reasonable for you to take me on my word right now because I've made promises before and failed. I realize I need to take some action, and here's what I plan to do..."
...insert your action plan here. Are you willing to commit to posting here daily? Are you willing to go to AA meetings for at least x times? Are you willing to research various stop-drinking methods? (AVRT is a good one, in my estimation - it's what DriGuy alludes to, even if he didn't read the book.) Are you willing to take antabuse every day for six months or even a year in the presence of your wife? (It will/should make you violently ill if you do drink.)
Of course, this is just one former wife's advise. Take it with a grain of salt. If you opt to share an action plan with her, it should be something that you are actually willing and able to commit to in the long-term; watch out for the over-promise/under-deliver equation - that's a surefire way to lose trust. Better to make no promises at all than to do that.